Quadratic Equations Questions

We provide quadratic equations practice exercises, instructions, and a learning material that allows learners to study outside of the classroom. We focus on quadratic equations skills mastery so, below you will get all questions that are also asking in the competition exam beside that classroom.

Quadratic Equations Questions

List of quadratic equations Questions

Question NoQuestionsClass
1If ( alpha ) and ( beta ) are the roots of ( a x^{2}+b x+ )
( c=0 ) then find the roots of the equation
( a x^{2}-b x(x-1)+c(x-1)^{2}=0 )
10
275. A boat goes 40 km upstream in 8
hours and 36 km downstream in
6 hours. The speed of the boat
in still water is
(1) 6.5 km/hour
(2) 5.5 km/hour
(3) 6 km/hour
(4) 5 km/hour
10
3If the one of the roots of the equation is zero find ‘a’
( boldsymbol{x}^{2}-2 boldsymbol{a} boldsymbol{x}+boldsymbol{a}^{2}+boldsymbol{a}-boldsymbol{2}=mathbf{0} )
Selective the positive answer.
10
4Find the roots of the equation ( x ) ( frac{1}{3 x}=frac{1}{6},(x neq 0) )10
5Solve the following equations:
( boldsymbol{x} boldsymbol{y}+boldsymbol{x}+boldsymbol{y}=boldsymbol{2} boldsymbol{3} )
( boldsymbol{x} boldsymbol{z}+boldsymbol{x}+boldsymbol{z}=boldsymbol{4} mathbf{1} )
( boldsymbol{y} boldsymbol{z}+boldsymbol{y}+boldsymbol{z}=mathbf{2 7} )
A. ( x=4,-2 ; y=2 ; 6 ; z=6,-5 )
в. ( x=2,-4 ; y=2,4 ; z=2,-6 )
c. ( x=5,-7 ; y=3,-5 ; z=6,-8 )
D. ( x=3,4 ; y=2,-5 ; z=2,-7 )
10
6If ( boldsymbol{a}(boldsymbol{p}+boldsymbol{q})^{2}+2 boldsymbol{b} boldsymbol{p} boldsymbol{q}+boldsymbol{c}=boldsymbol{0} ) and ( boldsymbol{a}(boldsymbol{p}+ )
( r)^{2}+2 p b r+c=0(a neq 0), ) then
A ( cdot q r=p^{2} )
B ( cdot q r=p^{2}+frac{c}{a} )
c. ( q r=-p^{2} )
D. None of the above
10
76.
(3x – 8)(3x+2)-(4x-11)(2x+1)=(x-3)(x + 7)
10
8Solve
( 3 x^{2}+20 x+8 )
10
9>
is
62. The difference of two factors for
the expression a4 + –
(1) -4 12) – 2
(3) 2
(4) 4
10
10Solve ( : 3^{4 x+1}-2 times 3^{2 x+2}-81=0 )
A. ( x=-3 )
B. ( x=9 )
c. ( x=-1 )
D. ( x=1 )
10
11The roots of the equation ( sqrt{3 x+1} ) ( mathbf{1}=sqrt{boldsymbol{x}} ) are
( mathbf{A} cdot mathbf{0} )
B.
c. ( 0, )
D. None
10
12The graph of an equation is given
above. What is the degree of the
polynomial?
( A )
B.
( c )
( D )
10
13The value of ( m ) for which one of the roots
of ( x^{2}-3 x+2 m=0 ) is double of one of
the roots of ( x^{2}-x+m=0 ) is
A . -2
B.
( c cdot 2 )
D. None of the above
10
14Add the following ( mathbf{2} p^{2} boldsymbol{q}^{2}-mathbf{3} boldsymbol{p} boldsymbol{q}+boldsymbol{4}=mathbf{0}, mathbf{5}+mathbf{7} boldsymbol{p} boldsymbol{q} )
( 3 p^{2} q^{2}=0 )
10
15Solve :
[
boldsymbol{x}^{2}-boldsymbol{8} boldsymbol{x}+mathbf{1 2}=mathbf{0}
]
10
16If ( a-b=1 ) and ( a b=12, ) find the value
of ( left(a^{2}+b^{2}right) )
10
17If the roots of the equation ( x^{2}+p x- )
( 6=0 ) are 6 and -1 then the value of ( p )
is
A . 2
B. 3
( c .-5 )
D. 5
10
18Determine the nature of roots of the
given quadratic equation ( 3 x^{2}+ ) ( mathbf{2} sqrt{mathbf{5}} boldsymbol{x}-mathbf{5}=mathbf{0} )
10
19Factorise
( 63 a^{2}-112 b^{2} )
10
20Find ( k, ) so that ( (k-12) x^{2}+2(k- )
12) ( x+2=0 ) has equal roots, where
( k neq 12 )
( mathbf{A} cdot k=4 )
B. ( k=12 )
c. ( k=14 )
D. none of these
10
217. If y = x2 + 2x – 3, y-x graph is
X
(6)
(c)
-3
-X
(d)

1-3
10
22Find the exact position solution of the
equation ( x^{2}+x=30 )
10
23If ( 4 y^{2}+4 y+1=0, ) then ( y=0 )
A. Yes
B. No
c. Ambiguous
D. Data insufficient
10
2424.
Let a, b, c be real numbers with a 70 and let a, ß be the roots
of the equation ax? + bx + c = 0. Express the roots of
aºx2 + abex + c = 0 in terms of a, B. (2001 – 4 Marks)
10
25The quadratic polynomial whose sum of
zeroes is 3 and product of zeroes is -2 is:
A ( cdot x^{2}+3 x-2=0 )
B . ( x^{2}-2 x+3=0 )
c. ( x^{2}-3 x+2=0 )
D. ( x^{2}-3 x-2=0 )
10
26The values of k for which the roots are
real and equal of the following equation ( 3 x^{2}-5 x+2 k=0 ) is
( k=frac{25}{24} )
A. True
B. False
10
27Find the values of ( K ) so that the
quadratic equations ( x^{2}+2(K-1) x+ )
( K+5=0 ) has atleast one positive root
A. ( k leq-1 )
B. ( k leq 1 )
c. ( k geq-1 )
D. ( -1 leq k leq 1 )
10
28The number of values ( k ) for which ( left[x^{2}-right. )
( left.(k-2) x+k^{2}right]left[x^{2}+k x+(2 k-1)right] ) is a
perfect square is
( A cdot 2 )
B.
( c cdot 0 )
D. None of these
10
29Let ( x=2 ) be a root of ( y=4 x^{2}-14 x+ )
( boldsymbol{q}=mathbf{0} . ) Then ( boldsymbol{y} ) is equal to
A ( cdot(x-2)(4 x-6) )
В. ( (x-2)(4 x+6) )
c. ( (x-2)(-4 x-6) )
D. ( (x-2)(-4 x+6) )
10
30Factorize:
( 2 m^{2}+39 m+19 )
10
31By increasing the speed of a car by 10 ( k m / h r, ) the time of journey for a distance of ( 72 k m ) is reduced by 36
minutes. Write an equation for the given information and check if it is a
Quadratic Equation?
10
32If 2,8 are the roots of ( x^{2}+a x+beta=0 )
and 3,3 are the roots of ( x^{2}+alpha x+b= )
0 then find the roots of ( x^{2}+a x+b=0 )
A . -1,-9
в. 1,9
c. -2,-8
D. 2,8
10
33If ( 3 x^{2}+10=11 x, ) then ( x=2, frac{5}{3} )
A. Yes
B. No
c. Ambiguous
D. Data insufficient
10
34Solve the given quadratic equation by using the formula method, ( (2 x+ )
( mathbf{3})(mathbf{2} boldsymbol{x}-mathbf{2})+mathbf{2}=mathbf{0} )
10
3571. There is a square field whose side
is 44 m. A square flowerbed is
prepared in its centre, leaving a
gravel path of uniform width all
around the flowerbed. The total
cost of laying the flowerbed and
gravelling the path at Rs. 2 and
Re. 1 per square metre respec-
tively is Rs. 3536. Find the width
of the gravelled path.
(1) 1 metre (2) 1.5 metre
(3) 2 metre (4) 2.5 metre
10
36Find the discriminant of the following quadratic equations and hence determine the nature of the roots of the
equation:
( frac{1}{4} x^{2}-2 x+1=0 )
10
37If the following quadratic equation has two equal and real roots then find the
value of ( mathrm{k}: )
( 4 x^{2}-5 x+k=0 )
10
38If ( (3-2 x) ) and ( (5 x+8) ) are factors of
( left(-10 x^{2}+h x-kright), ) then the values of ( h )
and ( k ) are respectively
A. -1 and 24
B. 1 and 24
c. -1 and -24
D. 1 and -24
10
39if ( alpha ) and ( beta ) are sum and product of roots of the given equation respectively, then
( (-boldsymbol{alpha} boldsymbol{beta}) ) is
A. always a prime number
B. always an odd integer
c. always an irrational number
D. dependent on value of a
10
40Determine the set of values of ( k ) for
which the given quadratic equation has
real roots:
( mathbf{2} boldsymbol{x}^{2}+boldsymbol{k} boldsymbol{x}-boldsymbol{4}=mathbf{0} )
10
41Find the value of ( p ) such that quadratic
equation ( (boldsymbol{p}-mathbf{1 2}) boldsymbol{x}^{2}-boldsymbol{2}(boldsymbol{p}-mathbf{1 2}) boldsymbol{x}+ )
( 2=0 ) has equal
10
42The positive root ( x^{2}+b x+8=0 ) is
twice the other root then ( b= )
A. 6
B. – –
c. 12
D. -12
10
43By selling an article for Rs.24, a trader
loses as much percent as the cost price of the article. Write an equation to express this information and check if it is convertible to a Quadratic Equation.
10
44( x^{2}+6 x+9=0 )
( x=? )
10
45If ( 6 x-x^{2}=1, ) then the value of ( (sqrt{x}- )
( left.frac{1}{sqrt{x}}right) ) is
( A cdot 2 )
B. 3
c. 1
D. –
10
46For the equation ( boldsymbol{x}^{2}-(boldsymbol{k}+mathbf{1}) boldsymbol{x}+left(boldsymbol{k}^{2}+right. )
( k-8)=0 ) if one root is greater then 2
and other is less than 2 , then ( k ) lies
between
A . ( -2 & 3 )
B. 2 & – 2
c. ( 2 &-3 )
D. None of these
10
47Solve for ( x: x^{5}+242=frac{243}{x^{5}}, ) where ( x ) is
real number.
10
48Find the discriminant for the given quadratic equation:
( boldsymbol{x}^{2}+boldsymbol{x}+mathbf{1}=mathbf{0} )
A . -3
B. – 5
( c .-7 )
D. – –
10
49If ( boldsymbol{h}=mathbf{5}, boldsymbol{k}=mathbf{3} ) then find the value of
( frac{k^{3}}{9}+frac{h k}{10} )
10
50Find the product of the roots of equation ( left(frac{x}{sqrt{2}}-2right)(x-sqrt{2})=0 )
( mathbf{A} cdot mathbf{4} )
B. 3
c. 2
( D )
10
5121. Let p,q e{1,2,3,4}. The number of equations of the form 3
px2 + qx+1=0 having real roots is
(1994)
(a) 15 (b) 9 (C) 7 let, (d) 8
10
52Check whether ( boldsymbol{x}^{2}+frac{1}{2} boldsymbol{x}=mathbf{0} ) is
a quadratic equation.
10
53Which of the following is not a quadratic equation
A ( cdot x-frac{3}{2 x}=5 )
в. ( 4 x-frac{5}{8}=x^{2} )
c. ( _{x+frac{1}{x}=9} )
D. ( 4 x-frac{2}{3 x}=4 x^{2} )
10
54Assertion
Let equations ( a x^{2}+b x+c= )
( mathbf{0}(boldsymbol{a}, boldsymbol{b}, boldsymbol{c} in boldsymbol{R}) & boldsymbol{x}^{2}+mathbf{2} boldsymbol{x}+mathbf{5}=mathbf{0} ) have
common root, then ( frac{boldsymbol{a}+boldsymbol{c}}{boldsymbol{b}}=frac{mathbf{1}}{mathbf{3}} )
Reason
If both roots of ( A x^{2}+B x+K_{1}=0 & )
( boldsymbol{A}^{prime} boldsymbol{x}^{2}+boldsymbol{B}^{prime} boldsymbol{x}+boldsymbol{K}_{2}=mathbf{0} ) are identical
( operatorname{then} frac{boldsymbol{A}}{boldsymbol{A}_{1}}=frac{boldsymbol{B}}{boldsymbol{B}_{1}}=frac{boldsymbol{K}_{1}}{boldsymbol{K}_{2}}left(text { where } boldsymbol{A}, boldsymbol{B}, boldsymbol{K}_{1}right. )
and ( left.A^{prime}, B,^{prime} K_{2} in Rright) )
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect, Reason is correct
10
55Roots of quadratic equation ( 5 x^{2}- ) ( 22 x-15=0 ) are
A ( cdot_{-5,} frac{-3}{5} )
в. ( _{5,} frac{3}{5} )
c. ( _{5}, frac{-3}{5} )
D. None of these
10
56If the roots of the equation ( 5 x^{2}-7 x+ )
( k=0 ) are mutually reciprocal then ( k= )
A . 5
B. 2
( c cdot frac{1}{5} )
D. None of these
10
57Find a two-digit number which exceeds
by 12 the sum of the squares of its digits and by 16 the doubled product of its digits.
10
58Find the value of ( K ), If the roots of the
following quadratic equation are equal ( : x^{2}+K x^{2}+1=0 )
10
59When will the quadratic equation
( boldsymbol{a} boldsymbol{x}^{2}+boldsymbol{b} boldsymbol{x}+boldsymbol{c}=boldsymbol{0} ) NOT have Real Roots?
A. ( b^{2}-4 a c geq 0 )
B . ( b^{2}-4 a c>0 )
c. ( b^{2}-4 a c<0 )
D. None of these
10
60If ( a, b, c ) are real and ( b^{2}-4 a c ) is perfect
square then the roots of the equation
( boldsymbol{a} boldsymbol{x}^{2}+boldsymbol{b} boldsymbol{x}+boldsymbol{c}=mathbf{0}, ) will be:
A. Rational & distinct
B. Real & equal
C. Irrational & distanct
D. Imaginary & distinct
10
61Given that ( z^{2}-10 z+25=9, ) what is ( z )
( ? )
A .3,4
в. 1,6
( c .2,6 )
D. 2,
10
62Find the roots using factorisation
( 9 x-x^{2}=0 )
A . 1,9
B. 0,9
( c .9,9 )
D.
10
63A two digit number is such that the product of its digits is ( 18 . ) When 63 is subtracted from the number, the digits interchange their places. Find the number10
64State the following statement is True or
False
The digit at ten’s place of a two digit number exceeds the square of digit at units place ( (x) ) by 5 and the number formed is ( 61, ) then the equation is
( mathbf{1 0}left(boldsymbol{x}^{2}+mathbf{5}right)+boldsymbol{x}=mathbf{6 1} )
A. True
B. False
10
65The two sides of a right-angled triangle are ( boldsymbol{x}, boldsymbol{x}+mathbf{1} ) and hypotenuse, the longest
side is ( sqrt{1} 3 . ) Find the area of the
triangle.
A ( cdot 1 mathrm{m}^{2} )
B. ( 2 mathrm{m}^{2} )
( c cdot 3 m^{2} )
D. ( 4 mathrm{m}^{2} )
10
66From ( 2012-2016, ) the amount (in crores)
spent on natural gas ( mathrm{N} ) and electricity ( mathrm{E} ) by Indian residents can be described by the following expressions, where t is the number of years since 2012 Gas spending model, ( mathrm{N}=2.13 t^{2}-4.21 t+37.40 )
Electricity spending model, ( mathrm{E}=-0.209 t^{2}+5.393 t+307.735 )
What is the total amount A spent on
natural gas and electricity by Indian residents from 2012 to 2016?
A. ( 1.467 t^{2}+7.423+121.721 )
1
B. ( 1.339 t^{2}-8.729 t+76.245 )
c. ( 1.01 t^{2}+7.083+97.83 )
D. ( 1.921 t^{2}+1.183 t+345.135 )
10
67If the roots of the equation ( x^{2}+p x+ )
( c=0 ) are (2,-2) and the roots of the
equation ( boldsymbol{x}^{2}+boldsymbol{b} boldsymbol{x}+boldsymbol{q}=mathbf{0} ) are ( (-mathbf{1},-mathbf{2}) )
then the roots of the equation ( x^{2}+ )
( b x+c=0 ) are
A ( .-3,-2 )
в. -3,2
c. 1,-4
D. -5,1
10
68For what values of ( k, ) the roots of the
quadratic equation ( (boldsymbol{k}+mathbf{4}) boldsymbol{x}^{2}+(boldsymbol{k}+ )
1) ( x+1=0 ) are equal?
10
6932. Let a, b, c be the sides of a triangle where a #bec and 2
R. If the roots of the equation
x2 +2(a+b+c)x +32 (ab + bc+ca)= 0 are real, then
(2006 – 3M, -1)
(6) and
10
70If the equation ( k x^{2}+4 x+1=0 ) has
real and distinct roots, then:
( mathbf{A} cdot k4 )
( mathbf{c} cdot k leqslant 4 )
D. ( k geqslant 4 )
10
71A train travels a distance of ( 480 k m ) at a
uniform speed. If the speed had been ( 8 k m / h r ) less, then it would have taken
3 hours more to cover the same
distance. Formulate the quadratic equation in terms of the speed of the train.
10
72Find the value ( frac{left(x^{2}-4right)}{(x+2)} )
A ( .2 x-2 )
B. ( x-2 )
c. ( x+2 )
D. None of these
10
73Find the nature of the roots of the
following quadratic equations. If the real roots exist, find them:
(i) ( 2 x^{2}-3 x+5=0 )
(ii) ( 3 x^{2}-4 sqrt{3} x+4=0 )
(iii) ( 2 x^{2}-6 x+3=0 )
10
74( sqrt{2} sec x+tan x=1 )10
75Check whether ( 3 x-10=0 ) is
a quadratic equation.
10
76For what value of ( k ) does ( (k-12) x^{2}+ )
( mathbf{2}=mathbf{0} ) have equal roots?
10
77Consider quadratic equation ( a x^{2}+ ) ( (2-a) x-2=0, ) where ( a in R )
If exactly one root is negative, then the
range of ( a^{2}+2 a+5 ) is
( A cdot[4, infty) )
B ( cdot[-2, infty) )
c. ( (-infty, 4] )
( D cdot(5, infty) )
10
7821. Let a, b, c be real. If ax2+bx+c=0 has two real roots a. and
B, where a 1, then show that 1++ <0.
a al
(1995 – 5 Marks)
where 24-1 med p21. then she was release
10
79If one of the roots of ( a x^{2}+b x+c=0 ) is
( mathbf{7}+sqrt{mathbf{2}} ) then find the other root
A. ( -7+sqrt{2} )
B. ( 7-sqrt{2} )
c. ( -7-sqrt{2} )
D. Cannot be determined
10
80Roots of the equation ( boldsymbol{x}^{3}-(boldsymbol{a}+boldsymbol{b}+ )
( c) x^{2}+(a b+b c+c a) x-a b c=0 )
( x^{2}+2 x+7=0 ) and ( a x^{2}+b x+c=0 )
have a common root, where ( a, b, c in R, ) can
be
A .4,8,28
В. 1,2,7
c. 1,4,36
D. None of the above
10
81Check whether ( 6 x^{3}+x^{2}=2 ) is
a quadratic equations
10
82The roots of ( x^{2}+k x+k=0 ) are real
and equal, find ( k )
10
83If ( x^{2}-b x+c=0 ) has equal integral
roots, then
This question has multiple correct options
A. ( b ) and ( c ) are integers
B. ( b ) and ( c ) are even integers
( mathrm{c} . b ) is an even integer and ( c ) is a perfect square of an integer
D. none of these
10
84Determine the nature of the roots of the
given equation from their discriminants.
( 2 y^{2}+11 y-7=0 )
A. Real and equal
B. Real and unequal
c. one real and one imaginary
D. Both imaginary
10
85Find ( p in R ) for ( x^{2}-p x+p+3=0 ) has
A. One positive and one negative root.
B. Both roots are negative
c. one root ( >2 ) and the other root ( <2 )
D. None of the above
10
86Find the value of ( k ) for which the given
equations has real and equal roots:
(i) ( (k-12) x^{2}+2(k-12) x+2=0 )
(ii) ( k^{2} x^{2}-2(k-1) x+4=0 )
10
87Find the discriminant of the equation and the nature of roots. Also find the
roots.
( 6 x^{2}+x-2=0 )
A ( cdot D=49, ) Real and distinct roots: ( frac{1}{5}, frac{-2}{3} )
B. ( D=39 ), Real and distinct roots: ( frac{1}{2}, frac{-2}{3} )
C. ( D=49 ), Real and distinct roots: ( frac{1}{3}, frac{-7}{3} )
D. ( D=49 ), Real and distinct roots: ( frac{1}{2}, frac{-2}{3} )
10
88The roots of the equation ( x^{2}-2 sqrt{2} x+ )
( mathbf{1}=mathbf{0} ) are-
A. Real and distinct
B. Imaginary and different
c. Real and equal
D. Rational and different
10
89The given quadratic equations have real roots and the roots are ( -sqrt{2}, frac{-5}{sqrt{2}} ) ( sqrt{2} x^{2}+7 x+5 sqrt{2}=0 )
A. True
B. False
10
90Amy is 5 years older than her sister Julie. If the product of their ages is 6 Find the age of Julie.
A. 1 year
B. 2 years
c. 3 years
D. 4 years
10
91Solve:6 ( +7 b-3 b^{2} )10
926. Ifx—2-2—2, then x is equal to?
x-2
10
93If ( x^{2}+a x+b ) is an integer for every
integer ( boldsymbol{x} ) then
A. ( a ) is always an integer but b need not be an integer
B. ( b ) is always an integer but a need not be an integer
( mathrm{c} cdot a+b ) is always an integer
D. none of these
10
94If the roots of the equation ( p x^{2}+q x+ )
( r=0 ) are in the ratio ( =l: m )
( left(l^{2}+m^{2}right) p r+l mleft(2 p r-q^{2}right)=0 )
10
95If the equation ( 16 x^{2}+6 k x+4=0 ) has
equal roots, then the value of ( k ) is
( mathbf{A} cdot pm 8 )
в. ( pm frac{8}{3} )
( c cdot_{pm frac{3}{8}} )
D. 0
10
96If ( x=2+2^{frac{1}{3}}+2^{frac{2}{3}}, ) then the values of
( boldsymbol{x}^{3}-mathbf{6} boldsymbol{x}^{2}+boldsymbol{6} boldsymbol{x} ) is
( mathbf{A} cdot mathbf{3} )
B. 4
( c cdot-2 )
D.
10
97If the equation ( x^{2}+4+3 cos (a x+ )
( b)=2 x ) has at least one solution where
( boldsymbol{a}, boldsymbol{b} in[mathbf{0}, mathbf{5}], ) then the value of ( (boldsymbol{a}+boldsymbol{b}) )
equal to
This question has multiple correct options
A ( .5 pi )
в. ( 3 pi )
c. ( 2 pi )
D.
10
98Write the Quadratic equation to find two consecutive odd positive integers, whose product is 32310
99Roots of the equations ( x^{2}-3 x+2=0 )
are
A. 1,-2
B . -1,2
c. -1,-2
D. 1,2
10
100If the roots of the equation
( (x-a)(x-b)+(x-b)(x-c)+ )
( (x-c)(x-a)=0 ) are equal, then
( a^{2}+b^{2}+c^{2} ) is equal to
( mathbf{A} cdot a+b+c )
B . ( 2 a+b+c )
c. ( 3 a b c )
D. ( a b+b c+c a )
E ( . a b c )
10
101The roots of the equation ( x^{2}+2 sqrt{3} x+ )
( mathbf{3}=mathbf{0} ) are
A . real and unequal
B. rational and equal
c. irrational and equal
D. irrational and unequal
10
10268. If p2 += 47, then the nu-
merical value of P+
will be
(1) 6
(2) 7
13) Ž
(4)
3
10
103Find the roots of each of the
following quadratic equations by the method of completing the squares
( 2 x^{2}-5 x+3=0 )
A. ( x=2, x=-7 )
В. ( x=-1, x=3 )
c. ( x=1, x=frac{3}{2} )
D. ( x=1, x=frac{1}{2} )
10
104If ( a<b<c<d, ) then for any real non-
zero ( lambda ), the quadratic equation ( (x- )
( a)(x-c)+lambda(x-b)(x-d)=0 ) has
This question has multiple correct options
A. Non-real roots
B. One real root between ( a ) and ( c ).
c. one real root between ( b ) and ( d )
D. Irrational roots.
10
105If the equation ( a x^{2}+2 b x+c=0 ) has
real roots, ( a, b, c ) being real numbers
and if ( m ) and ( n ) are real number such
that ( m^{2}>n>0 ) then show that the
equation ( a x^{2}+2 m b x+n c=0 ) has
real roots.
10
106expand:
( 9(x-y)^{2}+6(y-x) )
10
107The average weight of 15 Oarsmen in a
boat is increased by ( 1.6 mathrm{kg} ) when one of the crew, who weigh ( 42 mathrm{kg} ) is replaced
by a new man. Find the weight of the new man (in kg).
A . 65
B. 66
c. 43
D. 67
10
108The product of two consecutive integers is ( 600 . ) Find the second integer.
A .24
B . 23
c. 25
D. 26
10
109Is the following equation quadratic? ( mathbf{1 3}=-mathbf{5} boldsymbol{y}^{2}-boldsymbol{y}^{boldsymbol{3}} )
A. Yes
B. No
c. Ambiguous
D. Data insufficient
10
110The value of ( a ) for which the equation ( a^{2}+2 a+csc ^{2} pi(a+x)=0 ) has a
solution, is/are
( mathbf{A} cdot mathbf{0} )
B.
( c cdot-1 )
D.
10
111Solve for ( a, b )
( boldsymbol{a}^{2}+boldsymbol{b}^{2}-mathbf{4} boldsymbol{a}+mathbf{1 6} boldsymbol{b}+mathbf{6 8}=mathbf{0} )
10
112The values of ( k ) for which the equation
( 2 x^{2}+k x+x+8=0 ) will have real and
equal roots are
( A cdot 10 ) and -6
B. 7 and -9
( c cdot 6 ) and -10
D. -7 and 9
10
113If the roots of ( frac{1}{x+a}+frac{a}{x+b}=frac{1}{c}, ) are equal in magnitude and opposite in sign, then the product of the roots is :
A ( cdot-frac{1}{2}left(a^{2}+b^{2}right) )
B. ( frac{1}{2}left(a^{2}+b^{2}right) )
c. ( -frac{3}{2}left(a^{2}+b^{2}right) )
D. None
10
114If ( alpha ) and ( beta ) are two zeroes of the
polynomial ( boldsymbol{x}^{2}-mathbf{7} boldsymbol{x}+boldsymbol{k} ) where ( boldsymbol{alpha}-boldsymbol{beta}= )
( 5, ) find value of ( k )
10
115Divide:-
( boldsymbol{X}^{2}+mathbf{5} boldsymbol{X}+mathbf{6} boldsymbol{b} boldsymbol{y} boldsymbol{X}+mathbf{2} )
10
116For ( a, b, c in Q ) and ( b+c neq a, ) the roots of
( boldsymbol{a} boldsymbol{x}^{2}-(boldsymbol{a}+boldsymbol{b}+boldsymbol{c}) boldsymbol{x}+(boldsymbol{b}+boldsymbol{c})=mathbf{0} ) are
A. Rational and unequal
B. rational and equal
c. complex numbers
D. none
10
117Area enclosed by curves ( y=2^{x} ) and
( boldsymbol{y}=|boldsymbol{x}+mathbf{1}| ) in the first quadrant is?
A ( cdot frac{1}{2}-frac{1}{log 2} )
B. ( frac{3}{2}-frac{1}{2 log 2} )
c. ( frac{3}{2}-frac{1}{log 2} )
D. ( frac{1}{2}+frac{3}{log 2} )
10
118State the following statement is True or False

The length of a rectangle ( (x) ) exceeds its
breadth by ( 3 mathrm{cm} . ) The area of a rectangle is 70 sq.cm, then the equation is
( x(x-3)=70 )
A. True
B. False

10
119Solve the following equations:
( sqrt{4 x^{2}-7 x-15}-sqrt{x^{2}-3 x}= )
( sqrt{x^{2}-9} )
10
120If ( a x^{2}+b x+6=0 ) does not have two
distinct real roots, where ( boldsymbol{a} in boldsymbol{R}, boldsymbol{b} in boldsymbol{R} )
then the least value of ( 3 a+b ) is
A .4
B. – 1
( c .1 )
D. – 2
10
121If ( left(p^{2}-2 p+1right) x^{2}-left(p^{2}-3 p+2right) x+ )
( p^{2}-1=0 ) has more then two roots
then ( p= )
10
122The product of two consecutive integers is ( 156 . ) Find the integers.
A. 10 and 13
B. 12 and 13
c. 12 and 11
D. 1 and 13
10
123Three consecutive natural numbers are
such that the square of the middle number exceeds the difference of
squares of the other, two by ( 60 . ) Find the numbers.
10
124Find the roots
( 4 x^{2}+4 sqrt{3 x}+3=0 )
10
125Find the value of ( k ) for which the
equation ( 2 x^{2}-k x+3=0 ) will have
two real and equal roots.
10
126If ( a, b, c ) are non-zero, unequal rational
numbers, then the roots of the equation ( a b c^{2} x^{2}+left(3 a^{2}+b^{2}right) c x-6 a^{2}-a b+ )
( 2 b^{2}=0 ) are
A . rational
B. imaginary
C. irrational
D. none of these
10
127if sum=1 product ( =-6 ) then find the 2 numbers.10
128The length of a rectangle is ( 3 mathrm{cm} ) more than its width and area is ( 54 mathrm{cm}^{2} ). Find
the perimeter of the rectangle.
( mathbf{A} cdot 25 mathrm{cm} )
B. ( 30 mathrm{cm} )
c. ( 35 mathrm{cm} )
D. ( 40 mathrm{cm} )
10
129If ( r ) be the ratio of the roots of the
equation ( a x^{2}+b x+c=0, ) then ( frac{(r+1)^{2}}{r}= )
A ( cdot frac{a^{2}}{b c} )
в. ( frac{b^{2}}{c a} )
c. ( frac{c^{2}}{a b} )
D. None of these
10
1301
7.
4x +17
Solve: 18
13x – 2
17x-32
-=

x
3
=-
7x
12
x+16
36
10
131Check whether the given equation is a
quadratic equation or not. ( x^{2}+2 sqrt{x}-3 )
A. True
B. False
10
132Which of the following is not a quadratic equation?
A ( cdot x^{2}+6 y+2 )
B. ( (x-2)+(x+2)^{2}+3 )
c. ( (3 x-2)^{3}+frac{1}{2} x-4 )
D. ( 3 x^{2}-6 x+frac{1}{2} )
10
133If the roots of the equation ( x^{2}-2 a x+ )
( a^{2}+a-3=0 ) are real and less than 3
then
A ( . a<2 )
в. ( 2 leq a leq 3 )
c. ( 34 )
10
134Check whether the following is quadratic equation.
( boldsymbol{x}^{2}-mathbf{2} boldsymbol{x}=(-mathbf{2})(boldsymbol{3}-boldsymbol{x}) )
10
135Let ( boldsymbol{alpha}, boldsymbol{beta} ) be the roots of ( boldsymbol{a x}^{2}+boldsymbol{b x}+boldsymbol{c}= )
( 0 ; gamma, delta ) be the roots of ( p x^{2}+q x+r=0 )
and ( D_{1}, D_{2} ) are the respective
discriminants of these equations. If the
( boldsymbol{alpha}, boldsymbol{beta}, boldsymbol{gamma}, boldsymbol{delta} ) are in AP, then ( boldsymbol{D}_{1}: boldsymbol{D}_{2} ) is
equal to
( mathbf{A} cdot frac{a^{2}}{b^{2}} )
B. ( frac{a^{2}}{p^{2}} )
( ^{mathbf{C}} cdot frac{b^{2}}{q^{2}} )
D. ( frac{c^{2}}{r^{2}} )
10
136If ( alpha, beta ) are zeroes of polynomial ( f(x)= ) ( x^{2}+p x+q ) then polynomial having ( frac{1}{alpha} ) and ( frac{1}{beta} ) as its zeroes is:
A ( cdot x^{2}+q x+p )
B. ( x^{2}-p x+q )
c. ( q x^{2}+p x+1 )
D. ( p x^{2}+q x+1 )
10
137Sum of a number and its reciprocal is ( mathbf{5} frac{1}{mathbf{5}} . ) Then the required equation is
A ( cdot y^{2}+frac{1}{y}=frac{26}{5} )
B. ( 5 y^{2}-26 y+5=0 )
c. ( y^{2}+frac{1}{y}+frac{26}{5}=0 )
D. ( 5 y^{2}+26 y+5=0 )
10
138State the nature of the given quadratic
equation ( 3 x^{2}+4 x+1=0 )
A. Real and Distinct Roots
B. Real and Equal Roots
c. Imaginary Roots
D. None of the above
10
139For what value of ( mathrm{k} ), does the equation ( left[k x^{2}+(2 k+6) x+16=0right] ) have equal
roots?
A. 1 and 9
B. -9 and -1
c. -1 and 9
D. -1 and -9
10
140f ( x+y+z=0 ) then what is the value
of
( frac{1}{x^{2}+y^{2}-z^{2}}+frac{1}{y^{2}+z^{2}-x^{2}}+ )
( frac{1}{z^{2}+x^{2}-y^{2}} )
A ( cdot frac{1}{x^{2}+y^{2}+z^{2}} )
в.
c. -1
D.
10
141Solve the following quadratic equation by factorization, the roots are: ( 0, a+b ) ( frac{x-a}{x-b}+frac{x-b}{x-a}=frac{a}{b}+frac{b}{a} )
A. True
B. False
10
142If 8 is a root of the equation ( x^{2}-10 x+ )
( k=0, ) then the value of ( k ) is :
A . 2
B. 8
( c .-8 )
D. 16
10
143Find the nature of the roots of ( 3 x^{2}- )
( 4 sqrt{3} x+4=0 )
10
144The roots of the equation ( 2 x^{2}+x- )
( 4=0 ) are
( mathbf{A} cdot 1,-4 )
в. ( -3, frac{1}{sqrt{3}} )
c. ( frac{sqrt{33}-1}{4}, frac{-sqrt{33}-1}{4} )
D. None
10
145Solve ( frac{2 x+3}{2 x-3}+frac{2 x-3}{2 x+3}=frac{17}{4} )10
146The ( _{text {一一一一一一 }} ) product rule says that when the product of two terms is zero,
then either of the terms is equal to zero.
A. one
B. two
c. three
D. zero
10
147Given reason whether the following is an equation or not:
( (x-2)^{2}=x^{2}-4 x+4 )
10
148Solve :-
[
x^{2}-2 cos alpha+cos 2 alpha=0
]
10
149If the roots of ( left(a^{2}+b^{2}right) x^{2}-2 b(a+ )
( c) x+left(b^{2}+c^{2}right)=0 ) are equal, then
( a, b, c ) are in
A. A.P
в. G.P.
c. н.P.
D. none of these
10
150The roots of the following quadratic equation are not real ( 2 x^{2}-3 x+5=0 )
A . True
B. False
10
151I: If ( a, b, c ) are real, the roots of ( (b- )
( c) x^{2}+(c-a) x+(a-b)=0 ) are real
and equal, then ( a, b, c ) are in A.P.
Il: If ( a, b, c ) are real and the roots of ( left(a^{2}+right. )
( left.boldsymbol{b}^{2}right) boldsymbol{x}^{2}-boldsymbol{2} boldsymbol{b}(boldsymbol{a}+boldsymbol{c}) boldsymbol{x}+boldsymbol{b}^{2}+boldsymbol{c}^{2}=boldsymbol{0} ) are
real and equal, then ( a, b, c ) are in H.P.
Which of the above statement(s) is(are)
true?
A. only।
B. only II
c. both I and II
10
152Find the root of ( x^{2}-20 x+100 )10
153The roots of the equation ( x^{sqrt{x}}=(sqrt{x})^{x} )
are
A. 0 and 1
B. 0 and 4
c. 1 and 4
D. 0,1 and 4
10
154Solve the following quadratic equations by factorization method:
( mathbf{3}left(x^{2}-6right)=x(x+7)-3 )
A ( cdotleft{-frac{3}{2}, 5right} )
в. ( left{frac{3}{2}, 5right} )
( ^{c} cdotleft{-frac{3}{2},-5right} )
D. None of these
10
155Solve for ( x: sqrt{7 x^{2}}-6 x-13 sqrt{7}=0 )10
156Write the suitable quantifier for all
values of ( x ) there is no real number such
that ( x^{2}+2 x+2=0 )
A. Universal quantifier (forall)
B. Existential quantifier
c. Both
D. None
10
157If ( boldsymbol{alpha} neq boldsymbol{beta}, boldsymbol{alpha}^{2}=mathbf{5} boldsymbol{alpha}-mathbf{3}, boldsymbol{beta}^{2}=mathbf{5} boldsymbol{beta}-mathbf{3} )
then the equation whose roots are ( boldsymbol{alpha} / boldsymbol{beta} )
( & boldsymbol{beta} / boldsymbol{alpha} ) is
A ( cdot x^{2}+5 x-3=0 )
B. ( 3 x^{2}+12 x+3=0 )
c. ( 3 x^{2}-19 x+3=0 )
D. None of these
10
158Solve :
[
boldsymbol{x}^{2}+4 boldsymbol{x}+boldsymbol{4}=mathbf{0}
]
10
159Solve the equation obtained ( x^{2}-x- )
( 6=0 ) and hence find the dimensions of
the verandah. Verandah is in
rectangular shape having area and perimeter equal.
A. ( x=3 ; ) length ( =6 mathrm{m} ) and breadth ( =3 mathrm{m} )
B. ( x=3 ; ) length ( =6 mathrm{m} ) and breadth ( =4 mathrm{m} )
c. ( x=3 ; ) length ( =4 mathrm{m} ) and breadth ( =3 mathrm{m} )
D. ( x=4 ; ) length ( =6 mathrm{m} ) and breadth ( =3 mathrm{m} )
10
160Find the least positive value of ( k ) for
which the equation ( x^{2}+k x+4=0 )
has real roots.
10
16112. Which of the following is not the quadratic equation
whose roots are cosecand sec-e?
a. x2 – 6x + 6 = 0 b. x2 – 7x + 7 = 0
c. x2 – 4x + 4 = 0 d. none of these
10
162Find the roots of the equations by the method of completing the square. ( boldsymbol{x}^{2}+mathbf{7} boldsymbol{x}-mathbf{6}=mathbf{0} )10
163Determine whether the equation ( 5 x^{2}= )
( 5 x ) is quadratic or not.
A. Yes
B. No
c. complex equation
D. None
10
164fsum ( =-12, ) product ( =-28 . ) Then find the 2 numbers.10
16558. Two runners cover the samed
tance at the rate of 15 km a
16 km per hour respectively. Find
the distance travelled when one
takes 32 minutes longer than the
other.
(1) 128 km
(2) 64 km
(3) 96 km
(4) 108 km
10
166Solve ( 6 x^{2}-5 x-25=0 )10
167The following equation is a qudratic equation.
( 16 x^{2}-3=(2 x+5)(5 x-3) )
A. True
B. False
10
168If the roots of the equation ( p x^{2}+q x+ )
( boldsymbol{r}=mathbf{0} ) are in the ratio ( l: boldsymbol{m} ) prove that
( (l+m)^{2} p r=l m q^{2} )
10
169If ( n^{2}=(n+6), ) then find the value of ( n )
A. ( n=-2,-3 )
в. ( n=3,2 )
c. ( n=-3,2 )
D. ( n=-2,3 )
10
170A family is going to a theme park having ( t ) members in the family. Each ticket costs ( $ 80, ) and the number of
tickets needs to be bought can be
calculated from the expression ( t^{2}- )
( 4 t-90=6 ) when ( t>0 . ) What is the
total cost of the theme park tickets that
the family paid?
A. ( $ 640 )
B. ( $ 800 )
c. ( $ 960 )
D. ( $ 1,120 )
10
171The mentioned equation is in which form?
( mathbf{3} boldsymbol{y}^{2}-mathbf{7}=sqrt{mathbf{3}} boldsymbol{y} )
A. linear
B. Quadratic
c. Cubic
D. None
10
172The real values of ( a ) for which the
quadratic equation ( 2 x^{2}-left(a^{3}+8 a-right. )
1) ( x+a^{2}-4 a=0 ) possesses roots of opposite signs are given by :
( mathbf{A} cdot a>6 )
B . ( a>9 )
c. ( 0<a<4 )
D. ( a<0 )
10
173Which of the following is a Quadratic Equation?
A ( .5 x+8=0 )
B ( cdot 6 x^{2}+7 x=19 )
( mathbf{c} cdot x+1 )
D. None of these
10
174Solve ( x^{2}-6 x+2=0 )10
17513. If cosec -cot 0=, then the value of cosec O is
a. q+
1980
b. q- –
q
1
+ –
d. none of these
10
176Which of the following equations are not
quadratic?
( mathbf{A} cdot x(2 x+3)=x+2 )
B ( cdot(x-2)^{2}+1=2 x-3 )
( mathbf{c} cdot y(8 y+5)=y^{2}+3 )
D. ( y(2 y+15)=2left(y^{2}+y+8right) )
10
177John and jivanti together have 45 marbles. Both of them lost 5 marbles
each , and the product of the number of
marbles they now have is ( 128 . ) Form the quadratic equation.
10
178Solve the following. ( 3 a^{2} x^{2}+8 a b x+4 b^{2}=0,(a neq 0) )10
179Solve
( 4 x^{2}-7 x+5 )
10
180Say true or false.
f ( x(x-4)=0, ) then ( x=0 ) or ( x=4 )
A. True
B. False
10
181Check whether ( 2 x^{2}-3 x+5=0 ) has
real roots or no.
A. The equation has real roots.
B. The equation has no real roots.
c. Data insufficient
D. None of these
10
182The value ( (s) ) of ( k ) for which the
quadratic equation ( k x^{2}-k x+1=0 )
has equal roots is
( mathbf{A} cdot k=0 )
B. ( k=4 )
c. ( k=0,4 )
D. ( k=-4 )
10
183Say true or false.
( x^{2}+6=5 x, ) then ( x=3 ) or ( x=2 )
A. True
B. False
10
184Find the discriminant for the given equation:
( mathbf{3} boldsymbol{x}^{2}+mathbf{2} boldsymbol{x}-mathbf{1}=mathbf{0} )
A . 11
B. 13
c. 15
D. 16
10
185The roots of the equation ( a x^{2}+b x+ )
( c=0 ) will be in reciprocal if
( mathbf{A} cdot a=b )
B . ( a=b c )
( mathbf{c} cdot c=a )
D. ( c=b )
10
186Choose the quadratic equation in ( boldsymbol{p} )
whose solutions are 1 and 7
A ( cdot p^{3}-p x+6=0 )
B . ( p^{2}-p x+6=0 )
c. ( p^{2}-8 p+7=0 )
D. ( p^{2}-5 p+7=0 )
10
187Which of the following is a quadratic
equation?
( mathbf{A} cdot x^{frac{1}{2}}+2 x+3=0 )
B. ( left(x^{2}-1right)(x+4)=x^{2}+1 )
C ( cdot x^{2}-3 x+5=0 )
D. ( left(2 x^{2}+1right)(3 x-4)=6 x^{2}+3 )
10
188An equation whose maximum degree of variable is two is called ( ldots ). equation.10
189Let there be two integers such that one integer is 3 more than the other and
their product is ( 70 . ) Find the two integers.
A. 7 and 10
B. 6 and 9
c. 10 and 13
D. 12 and 14
10
190John and Jivanti together have 45 marbles. Both of them lost 5 marbles
each, and the product of the number of
marbles they now have is ( 124 . ) Form the quadratic equation we can find that John had 36 or 9 marbles.
A. True
B. False
10
191Solve ( 7 x^{2}-5 x-3=0 )10
192If ( alpha ) and ( beta ) are the roots of the equation
( x^{2}-p x+q=0, ) then find the equation whose roots are ( frac{boldsymbol{q}}{boldsymbol{p}-boldsymbol{alpha}} ) and ( frac{boldsymbol{q}}{boldsymbol{p}-boldsymbol{beta}} )
10
193Find a quadratic polynomial with ( frac{1}{4},-1 ) as the sum and product of its zeroes respectively.10
194Find ( a ) so that roots of ( x^{2}+2(3 a+ )
5) ( x+2left(9 a^{2}+25right)=0 ) are real.
10
195Determine the values of ‘ ( a^{prime} ) for which
both roots of the quadratic equation ( left(a^{2}+a-2right) x^{2}-(a+5) x-2=0 )
exceed the number minus one.
10
196Obtains all other zeroes of ( x^{4}-3 x^{3}- )
( x^{2}+9 x-6, ) if two of its zeroes are ( sqrt{3} )
and ( -sqrt{3} )
10
197If the value of ( b^{2}-4 a c^{prime} ) is greater than
zero, the quadratic equation ( a x^{2}+b x+ )
( c=0 ) will have
A. Two Equal Real Roots.
B. Two Distinct Real Roots.
c. No Real Roots.
D. No Roots or Solutions.
10
198The roots of the equation ( 2 y^{2}+y- )
( mathbf{2}=mathbf{0} ) are
A. ( frac{-1-sqrt{17}}{2}, frac{-1-sqrt{17}}{2} )
B. ( frac{-1-sqrt{17}}{4}, frac{-1+sqrt{17}}{4} )
c. ( -1-sqrt{17},-1+sqrt{17} )
D. None
10
199If the roots of the equation ( x^{2}-8 x+ )
( a^{2}-6 a=0 ) are real, then the value of ( a )
will be
A ( .-2<a<8 )
в. ( -2 leq a leq 8 )
( mathbf{c} cdot 2<a<8 )
D. ( 2 leq a leq 8 )
10
200The mentioned equation is in which form?
( (y-2)(y+2)=0 )
A. cubic
B. quadratic
c. linear
D. none of these
10
201STATEMENT -1: Roots of the quadratic equation ( 3 x^{2}-2 sqrt{6}+2=0 ) are same
STATEMENT -2: A quadratic equation
( a x^{2}+b x=c=0 ) has two distinct real
roots, if ( b^{2}-4 a c>0 )
A. Statement – 1 is True, Statement- – 2 is True, Statement 2 is a correct explanation for Statement – 1
B. Statement – 1 is True, Statement – 2 is True : Statement 2 is NOT a correct explanation for Statement- –
c. statement- 1 is True, Statement – 2 is False
D. Statement-1 is False, Statement- – 2 is True
10
202A root of the equation ( (x-1)(x- )
2) ( =frac{30}{49} ) is
A ( -frac{17}{7} )
B. ( frac{15}{7} )
c. ( frac{13}{7} )
D. ( frac{11}{7} )
10
203Solve
[
boldsymbol{x}^{2}+mathbf{5}=-mathbf{6} boldsymbol{x}
]
10
204Assertion (A): The roots of ( (x-a)(x- )
( b)+(x-b)(x-c)+(x-c)(x-a)= )
0 are real
Reason (R): A quadratic equation with non-negative discriminant has real
roots
A. Both (A) and (R) are true and (R) is the correct explanation of (A)
B. Both (A) and (R) are true and (R) is not the correct explanation of ( (A) )
( c cdot(A) ) is true but (R) is false
D. (A) is false but (R) is true
10
205Find the roots of the following quadratic equation, if they exist, using the quadratic formula of Shridhar Acharya. ( 2 x^{2}-2 sqrt{2} x+1=0 )10
206If ( a+b+c=2 s, ) then the value of ( (s- )
( a)^{2}+(s-b)^{2}+(s-c)^{2} ) will be
A ( cdot s^{2}+a^{2}+b^{2}+c^{2} )
B. ( a^{2}+b^{2}+c^{2}-s^{2} )
c. ( s^{2}-a^{2}-b^{2}-c^{2} )
D. ( 4 s^{2}-a^{2}-b^{2}-c^{2} )
10
207If the product of all solution of the equation ( frac{(2009) x}{2010}=(2009)^{log _{x}(2010)} ) can
be expressed in the lowest form as ( frac{m}{n} ) then the value of ( (boldsymbol{m}+boldsymbol{n}) ) is
10
208Factorise ( : boldsymbol{m}^{2}-mathbf{1 0 m}-mathbf{1 4 4} )10
209Thrice the square of a natural number decreased by 4 times the number is
equal to 50 more than the number. The number is
( A cdot 4 )
B. 5
( c cdot 6 )
D. 10
10
210Which of the following equations has two distinct real roots ?
A ( cdot 2 x^{2}-3 sqrt{2} x+frac{9}{4}=0 )
В. ( x^{2}+x-5=0 )
c. ( x^{2}+3 x+2 sqrt{2}=0 )
D. ( 5 x^{2}-3 x+1=0 )
10
211Solve ( : a^{2}-(b+5) a+5 b=0 )10
212In solving a problem, one student makes a mistake in the coefficient of
the first degree term and obtains -9
and -1 for the roots. Another student
makes a mistake in the constant term
of the equation and obtains 8 and 2 for the roots. The correct equation was?
A. ( x^{2}+10 x+9=0 )
B . ( x^{2}-10 x+16=0 )
c. ( x^{2}-10 x+9=0 )
D. None of the above
10
213If ( a=frac{1}{3-2 sqrt{2}}, b=frac{1}{3+2 sqrt{2}} ) then the value
of ( boldsymbol{a}^{mathbf{3}}+boldsymbol{b}^{mathbf{3}} ) is:
A ( cdot 194 )
B. 200
c. 198
D. 196
10
214For what positive values of ‘ ( m ) ‘ roots of given equation
is equal, distinct, imaginary ( boldsymbol{x}^{2}- )
( boldsymbol{m} boldsymbol{x}+boldsymbol{9}=mathbf{0} )
10
215Let ( f(x)=x^{2}-3 x+4, ) then the value
of ( boldsymbol{x} ) which satisfies ( boldsymbol{f}(mathbf{1})+boldsymbol{f}(boldsymbol{x})= )
( boldsymbol{f}(mathbf{1}) boldsymbol{f}(boldsymbol{x}) ) is
A .
B.
c. 1 or 2
D. 1 and 0
10
216The sum of the values of k for which the
roots are real and equal of the following equation ( 4 x^{2}-2(k+1) x+(k+4)=0 ) is
10
217Is the given equation quadratic? Enter 1 for True and 0 for False.
( boldsymbol{x}^{2}+boldsymbol{4} boldsymbol{x}=mathbf{1 1} )
10
218Find the value of ( k ) for which the
equation ( boldsymbol{x}^{2}+boldsymbol{k}(boldsymbol{2} boldsymbol{x}+boldsymbol{k}-mathbf{1})+boldsymbol{2}=mathbf{0} )
has real and equal roots.
10
219The product of two consecutive natural
numbers is ( 12 . ) The equation form of this statement is
A. ( x^{2}+2 x-12=0 )
B . ( x^{2}+1 x-12=0 )
c. ( x^{2}+1 x+12=0 )
D. ( x^{2}+2 x+12 )
10
220The value of ( a ) for which one root of the
quadratic equation ( left(a^{2}-5 a+3right) x^{2}+ )
( (3 a-1) x+2=0 ) is twice as large as the other is
A ( cdot-frac{2}{3} )
в. ( frac{1}{3} )
( c cdot-frac{1}{3} )
D. ( frac{2}{3} )
10
221Find the discriminant of the equation
and the nature of roots. Also find the
roots, if they are real:
( 3 x^{2}-2 x+frac{1}{3}=0 )
A. Roots are imaginary
B. ( mathrm{D}=0, ) Roots are real and equal ( frac{1}{3}, frac{1}{3} )
( mathrm{c} cdot_{mathrm{D}=} frac{2}{5}, ) Roots are real and unequal ( frac{1}{5}, frac{1}{2} )
D. Cannot be determined
10
222Find the roots of each of the
following quadratic equations by the method of completing the squares ( sqrt{5} x^{2}+9 x+4 sqrt{5}=0 )
A. ( -sqrt{7}, frac{-17}{sqrt{3}} )
в. ( -sqrt{5}, frac{-4}{sqrt{5}} )
c. ( -sqrt{5}, frac{-14}{sqrt{3}} )
D. ( -sqrt{7}, frac{-13}{sqrt{5}} )
10
2231 U0 WUL LUI DU
16. Let a, b, c be real numbers, a = 0.
o, c be real numbers, a = 0. If a is a root of
+bx+c = 0. B is the root of a2x2 – bx -c= 0 and
0<a<B, then the equation a2x2 +2bx +2c=0 has a root y
that always satisfies
(1989- 2 Marks)
(a)
=
(b) y = a +5
(d) a <y<B.
(c) yra
10
224Check whether ( x^{2}-frac{29}{4} x+5=0 ) is
a quadratic equation
10
225Let ( p, q in{1,2,3,4} . ) The number of
equation of the form ( p x^{2}+q x+1=0 )
having real roots, is
A . 15
B. 9
c. 8
D. 7
10
226The number of real roots of the
equation ( (x-1)^{2}+(x-2)^{2}+(x- )
( mathbf{3})^{2}=mathbf{0} ) is :
( mathbf{A} cdot mathbf{1} )
B . 2
( c .3 )
D. None of these
10
227f ( p ) and ( q ) are positive then the roots of the equation ( x^{2}-p x-q=0 ) are
A. imaginary
B. real & both positive
c. real & both negative
D. real & of opposite sign
10
2285. Find the solution for
5.
Find the solution for
10
229The graph of ( boldsymbol{p}(boldsymbol{x})=boldsymbol{x}^{2}-boldsymbol{4} boldsymbol{x}+boldsymbol{3} )
represents
A. a line segment
B. parabola
c. a line
D. a ray
10
230If ( 3 x^{2}+4 k x+1>0 ) for all real values
of ( x, ) then ( k ) lies in the interval.
A ( cdotleft(frac{-sqrt{3}}{2}, frac{sqrt{3}}{2}right) )
в. ( left(frac{-1}{4}, frac{1}{4}right) )
( ^{c} cdotleft[frac{-sqrt{3}}{2}, frac{sqrt{3}}{2}right] )
D. ( left(frac{-1}{2}, frac{1}{2}right) )
10
231Which of the following is quadratic polynomial
( mathbf{A} cdot x+2 )
B. ( x^{2}+2 )
c. ( x^{3}+2 )
D. ( 2 x+2 )
10
232The formula of discriminant of
quadratic equation ( a x^{2}+b x+c=0 ) is
( D= )
10
233In a square box, a glass is to be surrounded by a ( 2 mathrm{cm} ) glass border. If
the total area of the square is ( 121 mathrm{cm}^{2} ) Find the dimension of the glass box.
A. ( 5 mathrm{cm} )
в. ( 6 mathrm{cm} )
( c cdot 7 mathrm{cm} )
D. ( 8 mathrm{cm} )
10
234Verify:
( (a+b)^{2}-(a-b)^{2}=4 a b, ) for ( a= )
( mathbf{4}, boldsymbol{b}=mathbf{3} )
10
235For what value of ( ^{prime} boldsymbol{k}^{prime},left(boldsymbol{k}^{2}-mathbf{4}right) boldsymbol{x}^{2}+ )
( 2 x-9=0 ) can not be quadratic
equation?
10
236Solve the following quadratic equation
for ( x )
( 4 x^{2}+4 b x-left(a^{2}-b^{2}right)=0 )
10
237Solve the equation ( mathbf{5}^{x^{2}+3 x+2}=mathbf{1} )
find the difference between the roots of
the equation.
10
238If the area of rectangle is given by ( x^{2}+ ) ( 5 x+6 ) then write the possible length
and breadth.
10
239The Discriminant value of equation ( mathbf{5} boldsymbol{x}^{2}-mathbf{6} boldsymbol{x}+mathbf{1}=mathbf{0} ) is
A . 16
B. ( sqrt{56} )
( c cdot 4 )
D. 56
10
240Determine the nature of roots of the
equation ( x^{2}+2 x sqrt{3}+3=0 )
A. Real and distinct
B. Non-real and distinct
c. Real and equal
D. Non-real and equal
10
241Check whether the given equation is a quadratic equation
( x+frac{3}{x}=x^{2} )
10
242Determine the nature of the roots of the
follwoing quadratic equation:
( 2 x^{2}-6 x+3=0 )
10
243( frac{1}{(x-1)(x-2)}+frac{1}{(x-2)(x-3)}= )
( frac{2}{3}, x neq 1,2,3 . ) Find sum of values of ( x )
10
244Solve the given quadratic equation by
factorization method
( boldsymbol{x}^{2}-mathbf{9}=mathbf{0} )
10
245Find the roots of the quadratics equation ( 3 x^{2}-4 sqrt{3} x+4=0 )10
246Solve
( 6 m^{2}-11 m+6=0 )
10
247If ( a<c<b ) then the roots of the
equation ( (a-b)^{2} x^{2}+2(a+b- )
( 2 c) x+1=0 ) are
A. Imaginary
B. Real
c. one real and one Imaginary
D. Equal and Imaginary
10
248If the roots of ( a x^{2}-b x-c=0 ) change
by the same quantity, then the expression in ( a, b, c ) that does not
change is
A ( cdot frac{b^{2}-4 a c}{a^{2}} )
в. ( frac{b-4 c}{a} )
c. ( frac{b^{2}+4 a c}{a^{2}} )
D. none of these
10
249Find the value of ( k ) for which the
equation ( x^{2}-6 x+k=0 ) has distinct
roots.
( mathbf{A} cdot k>9 )
B. ( k=6,7 ) only
c. ( k<9 )
( mathbf{D} cdot k=9 )
10
250Solve by factorization ( sqrt{mathbf{3}} boldsymbol{x}^{2}+mathbf{1 1} boldsymbol{x}+ )
( mathbf{6} sqrt{mathbf{3}}=mathbf{0} )
10
251The number of points ( (p, q) ) such that
( boldsymbol{p}, boldsymbol{q} in{1,2,3,4} ) and the equation
( p x^{2}+q x+1=0 ) has real roots is
( A cdot 7 )
B. 8
c. 9
D. none of these
10
252State the following statement is True or
False

The sum of a natural number ( x ) and its
eciprocal is ( frac{37}{6}, ) then the equation is ( boldsymbol{x}+frac{mathbf{1}}{boldsymbol{x}}=frac{mathbf{3 7}}{mathbf{6}} )
A. True
B. False

10
253Solve
( 12 x^{2}-27=0 )
10
254Calculate ( frac{1}{x_{1}^{3}}+frac{1}{x_{2}^{3}}, ) where ( x_{1} ) and ( x_{2} )
are roots of the equation ( 2 x^{2}-3 a x- )
( mathbf{2}=mathbf{0} )
10
255For what value of ( k,(4-k) x^{2}+ )
( (2 k+4) x+(8 k+1)=0 ) is a perfect
square:
10
25618. Let a, ß be the roots of the equation (x-a)(x-6)=c,c*0.-
Then the roots of the equation
(x-a) (x-B)+c=0 are
(1992 – 2 Marks)
(a) a,
(b) b,c
(c) a b
(d) at c,b+c
10
257Find the value ( (s) ) of ( k ) so that the
equation ( x^{2}-11 x+k=0 ) and ( x^{2}- )
( 14 x+2 k=0 ) may have a common root.
10
258Figure shows a square with total area of
121 square units. Calculate the value of
( boldsymbol{x} )
begin{tabular}{|c|c|}
hline & \
( 7 x ) & 49 \
hline( x^{2} ) & ( 7 x ) \
hline
end{tabular}
( A )
B.
( c )
D. 1
( E )
10
259Solve ( 2 cos ^{2} theta-sqrt{3} sin theta+1=0 )10
260I: The roots of ( a(b-c) x^{2}+b(c-a) x+ )
( c(a-b)=0 ) are real and equal, then
( a, b, c ) are in G.P.
II: The number of solutions of ( mid x^{2}- ) ( 2 x+2 mid=3 x-2 ) is 4
Which of the above statement(s) is/are
true?
A. only।
B. only II
c. both I and II
D. neither I nor II
10
261If the roots of a quadratic expression
( a x^{2}+b x+c ) are complex, then
A ( cdot b^{2}4 a c )
c. ( b^{2}=4 a c )
( mathbf{D} cdot a=0 )
10
262Solve: ( sqrt{7 sqrt{7 sqrt{7 sqrt{7 sqrt{7 ldots ldots}}}}}=k . ) Find k.10
263If
( a, b, c ) are real numbers such that ac
( neq 0, ) then show that at least one of the
equations ( a x^{2}+b x+c=0 ) and ( -a x^{2}+b x )
( +c=0 ) has real roots.
10
264Factorise: ( 5 x^{2}-x-4 )10
26571.
1+2 72 + 73 73+ 74
will be equal to
(1) 1
(2) -3
(3) Both of above
(4) None of the above
10
266Solve: ( boldsymbol{x}+frac{mathbf{1}}{boldsymbol{x}}=mathbf{5} )10
267The values of he equation afor which
both the roots of the equation ( (a- )
6)( x^{2}=a(x-3) ) are positive are given
by
в. ( left(0, frac{72}{11}right) )
c. ( left(6, frac{72}{11}right) )
D. ( left(frac{72}{13}, 6right) )
10
268The number of point of intersection of the two curves ( y=2 sin x ) and ( y= )
( 5 x^{2}+2 x+3 ) is ( ? )
( A cdot infty )
B. 0
c. 1
D. less than two
10
269If ( a ) and ( b ) are the roots of ( x^{2}-p x+q= )
( 0, ) then ( a^{2}+b^{2} ) is
A ( cdot p^{2}+q^{2} )
B . ( p^{2}+2 q )
c. ( p^{2}-q^{2} )
D. ( p^{2}-2 q )
10
270if ( [mathrm{x}] ) is the integral part of ( mathrm{x} ), then solve ( left[mathbf{4}-[boldsymbol{x}]^{2}right]-[boldsymbol{x}]^{2}=mathbf{2} )
find the number of integers satisfying
the equation.
10
271Which of the following statements has
the truth value ( ^{prime} F^{prime} ? )
A. A quadratic equation has always a real root
B. The number of ways of seating 2 persons in two chairs out of ( n ) persons in ( P(n, 2) )
C. The cube roots of unity are in GP
D. None of the above
10
272Determine ( k ) for which the quadratic
equation has equal roots ( k x^{2}-5 x+ )
( boldsymbol{k}=mathbf{0} )
10
273If ( frac{1}{a}+frac{1}{b}+frac{1}{c}=frac{1}{a+b+c} ) where ( (a+ )
( b+c) neq 0 ) and ( a b c neq 0 . ) What is the
value of ( (boldsymbol{a}+boldsymbol{b})(boldsymbol{b}+boldsymbol{c})(boldsymbol{c}+boldsymbol{a}) ? )
( mathbf{A} cdot mathbf{0} )
B.
( c cdot-1 )
( D )
10
274Find the value of ‘p’ for which the
quadratic equatio has equal roots, ( (p+1) n^{2}+2(p+3) n+(p+8)=0 )
10
275Simplify ( frac{a}{x-a}+frac{b}{x-b}=frac{2 c}{x-c} )10
2762.
A number which satisfies the given equation is called
solutions or root of the equation.
10
27718. For a s 0, determine all real roots of the equation
x2 – 2a x – al-3a2 = 0
(1986 – 5 Marks)
10
278If the roots of the equation ( x^{2}-15- )
( boldsymbol{m}(mathbf{2} boldsymbol{x}-mathbf{8})=mathbf{0} ) are equal, then ( boldsymbol{m}= )
A. 3,-5
в. 3,5
c. -3,5
D. -3,-5
10
279For ( a>0, ) all the real roots of the
equation ( boldsymbol{x}^{2}-mathbf{3} boldsymbol{a}|boldsymbol{x}-boldsymbol{a}|-mathbf{7} boldsymbol{a}^{2}=mathbf{0} ) are
( mathbf{A} cdot 4 a, 5 a )
в. ( -4 a, 5 a )
( mathbf{c} .-4 a,-5 a )
D. ( 4 a,-5 a )
10
280If one root of ( x^{2}-x-k=0 ) is square of
the other, then ( k= )
A ( .2 pm sqrt{5} )
B . ( 2 pm sqrt{3} )
( c cdot 3 pm sqrt{2} )
D. ( 5 pm sqrt{2} )
10
281For what value of ( k ) will the quadratic
equation: ( k x^{2}+4 x+1=0 ) have real
and equal roots?
A .2
B. 3
( c cdot 4 )
( D )
10
28271. Which one of the following is a
root of equation x + x + 1 = 0?
(1) x=0 (2) x= 1
(3) Both of above
(4) none of the above
10
283If ( A ) and ( B ) are whole numbers such that
( 9 A^{2}=12 A+96 ) and ( B^{2}=2 B+3, ) find
the value of ( 5 A+7 B )
A . 31
B. 37
c. 41
D. 43
10
284Find the quadratic equation in ( x, ) whose
solutions are 3 and 2
A ( cdot x^{3}-5 x+6=0 )
B. ( x^{2}-5 x+6=0 )
c. ( x^{2}-3 x+6=0 )
D. ( x^{2}-5 x+7=0 )
10
285The product of two consecutive even
numbers is ( 120 . ) Can you express this information in the form of a Quadratic
Equation? If yes, what would be the resulting Quadratic Equation?
10
286Show that the equation ( 2left(a^{2}+b^{2}right) x^{2}+ )
( 2(a+b) x+1=0 ) has no real roots,
when ( a neq b )
10
287The area of a rectangular field is given
as 300 square metres. It is also given that the breadth of the field is 3 metres
more than its length. Can this
information be expressed mathematically as a Quadratic
Equation. If yes, what would be the resulting Quadratic Equation?
10
288f ( a, b, c in R^{+} ) and ( 2 b=a+c, ) then
check the nature of roots of equation ( boldsymbol{a} boldsymbol{x}^{2}+boldsymbol{2} boldsymbol{b} boldsymbol{x}+boldsymbol{c}=mathbf{0} )
10
289One year ago a man was eight times old as his son. Now his age is equal to the square of his son’s age. Represent this situation in form of a quadratic equation10
290Solve:
( 28-31 x-5 x^{2}=0 )
10
291All the values of ‘a’ for which the
quadratic expression ( a x^{2}+(a- )
2) ( x-2 ) is negative for exactly two
integral values of ( x ) may lie in
A. ( (1,3 / 2) )
B. ( (3,2 / 2) )
c. (1,2)
(i) 5
D. (-1,2)
10
292f ( a(a+2)=24 ) and ( b(b+2)=24 )
where ( a neq b, ) then ( a+b= )
A . – 48
B . – –
( c cdot 2 )
D. 46
E. 48
10
2931.
If l, m, n are real, em, then the roots by the equation:
(l-mx2–5 (+ m)x-2 (1-m)=0 are (1979)
(a) Real and equal
(6) Complex
(c) Real and unequal
(d) None of these.
10
294Solve the following quadratic equation by factorization, the roots are ( boldsymbol{x}^{2}-(sqrt{mathbf{3}}+mathbf{1}) boldsymbol{x}+sqrt{mathbf{3}}=mathbf{0} )
A . 3,1
в. ( sqrt{2}, )
c. ( sqrt{3}, 1 )
D. ( sqrt{5}, )
10
295If ( frac{5 x-7 y+10}{1}=frac{3 x+2 y+1}{8}= )
( frac{11 x+4 y-10}{9}, ) then what is the ( x+y )
equal to?
A . 1
B. 2
( c cdot 3 )
D. –
10
296Find the value of ‘k’ so that the equation
( boldsymbol{x}^{2}+mathbf{4} boldsymbol{x}+(boldsymbol{k}+mathbf{2})=mathbf{0} ) has one root
equal to zero.
10
297The value of k for which the quadratic
equation, ( k x^{2}+1=k x+3 x-11 x^{2} )
has real and equal roots are
A. ( -11 .-3 )
3 ( 3.31-31-3 )
B. 5,7
c. 5,-7
D. None of these
10
2984.
If (y – 4)² = 16 then find the value of y.
10
10
299The rectangular fence is enclosed with an area ( 16 mathrm{cm}^{2} . ) The width of the field is
( 6 mathrm{cm} ) longer than the length of the fields.
What are the dimensions of the field?
A. length ( =2 mathrm{cm}, ) width ( =6 mathrm{cm} )
B. length ( =1 mathrm{cm}, ) width ( =8 mathrm{cm} )
c. length ( =2 mathrm{cm}, ) width ( =8 mathrm{cm} )
D. length ( =3 mathrm{cm}, ) width ( =8 mathrm{cm} )
10
300If one of the zeroes of the quadratic
polynomial ( (k-1) x^{2}+k x+1 ) is -3
then the value of ( k ) is.
A ( cdot frac{4}{3} )
в. ( frac{-4}{3} )
( c cdot frac{2}{3} )
D. ( frac{-2}{3} )
10
301What is the absolute value of the difference
between the roots of ( x^{2}+6 x+5=0 ? )
10
302If the roots of the quadratic equation
( x^{2}+6 x+b=0 ) are real and distinct
and they differ by atmost 4 then the least value of ( b ) is
A . 5
B. 6
( c cdot 7 )
D. 8
10
303f ( p, q, r ) are real and ( p neq q, ) then roots of
the equation ( (boldsymbol{p}-boldsymbol{q}) boldsymbol{x}^{2}+mathbf{5}(boldsymbol{p}+boldsymbol{q}) boldsymbol{x}- )
( mathbf{2}(boldsymbol{p}-boldsymbol{q})=mathbf{0} ) are
A. Real and equal
B. Complex
c. Real and unequal
D. None of these
10
30458. I 2×2 +5x+2, value of
1) 2
(3) -2
(4-2
10
305Check whether the following is Quadratic equations:
( (x+1)^{2}=2(x-3) )
10
306Find a quadratic equation with real coefficient whose one root is ( 3-2 i )10
307Two candidates attempt to solve a
quadratic equation of the ( a x^{2}+b x+ )
( c=0 ) One starts with a wrong value of ( b )
and find the roots to be 2 and 6 . The
other starts with the wrong values of ( c )
and find the roots to be ( +2,-9 . ) The correct roots of the equation are
10
308( sqrt{x^{2}+1} )10
30920. Solve
? +4x+31 +2x + 5 = 0
(1988 – 5 Marks)
10
310Factorize ( 3 x^{2}+14 x+15 )10
311Solve the equation using formula. ( 2 x^{2}+frac{x-1}{5}=0 )
A ( cdot x=frac{-1 pm sqrt{10}}{4} )
B. ( x=frac{-1 pm sqrt{41}}{20} )
c. ( x=frac{1 pm sqrt{41}}{20} )
D. ( _{x}=frac{1 pm sqrt{10}}{4} )
10
312Factorise: ( 12 a x-4 a b+18 b x-6 b^{2}= )
0
10
313Find the values of ( k ) for which the given equation has real and equal roots ( mathbf{2} boldsymbol{x}^{2}-mathbf{1} mathbf{0} boldsymbol{x}+boldsymbol{k}=mathbf{0} )10
31453. If (3a + 1)2 + (b – 1)2 + (20-3)2
= 0, then the value of
(3a + b + 2c) is equal to :
(1) 3 (2)-1
(3) 2
(4)5
10
315If ( x ) is real, ( x+frac{1}{x} neq 0 ) and ( x^{3}+frac{1}{x^{3}}=0 )
then the value of ( left(boldsymbol{x}+frac{mathbf{1}}{boldsymbol{x}}right)^{mathbf{4}} ) is
( mathbf{A} cdot mathbf{4} )
B. 9
c. 16
D. 25
10
316If ( x=5+2 sqrt{6}, ) then the value of
( left(sqrt{boldsymbol{x}}-frac{1}{sqrt{x}}right)^{2} )
A ( .4 sqrt{6} )
B. 8
c. 16
D. 12
E. None of these
10
317( mathbf{f} boldsymbol{x}=frac{1}{mathbf{5}+frac{mathbf{1}}{mathbf{5}+frac{mathbf{1}}{mathbf{5}+} cdots cdots}}^{text {then }} )
A ( cdot x^{2}+5 x-1=0 )
B . ( x^{2}-5 x-1=0 )
C ( cdot x^{2}-5 x+1=0 )
D. ( x^{2}+5 x+1=0 )
10
318( frac{41 x-12}{x^{2}-16}=frac{4 x+3}{x-4} )10
31963. The value of
20+ V20 + 120+……. is:
(1) 4 (2) 3 h
(3) 5
(4) 0
10
320A two-digit number is such that the product of its digits is 8. When 18 is subtracted from the number, the digits interchange their places. Find the number.10
321If one root of the equation ( x^{2}+p x+ )
( 12=0 ) is 4 while the equation ( x^{2}+ )
( p x+q=0 ) has equal roots, then one
value of ( q ) is
( mathbf{A} cdot mathbf{3} )
в. 12
c. ( frac{49}{4} )
D. 4
10
322( x^{2}+(a+b+c) x+a b+b c )10
323If ( a-b=5 ) and ( a^{2}+b^{2}=53, ) find the
value of ( a b )
10
324( boldsymbol{x}^{2}+mathbf{5} boldsymbol{x}-left(boldsymbol{a}^{2}+boldsymbol{a}-boldsymbol{6}right)=mathbf{0} )10
325A farmer wishes to start a 100 sq.m
rectangular vegetable garden. since he has only ( 30 mathrm{m} ) barbed wire, he fences the sides of the rectangular garden letting his house compound wall act as the fourth side fence. Find the
dimension of the garden.
A. ( 20 m, 5 m ) or ( 10 m, 10 m )
В. ( 2 m, 5 m ) or ( 10 m, 10 m )
( mathrm{c} .20 mathrm{m}, 5 mathrm{m} ) or ( 1 mathrm{m}, 10 mathrm{m} )
D. None of these
10
326Is the following equation a quadratic equation?
( 16 x^{2}-3=(2 x+5)(5 x-3) )
A. Yes
B. No
c. Ambiguous
D. Data insufficient
10
327( f(m)=2, ) find the value of ( m^{2}-m+1 )10
328The value of ( mathrm{k} ) for which polynomial
( x^{2}-k x+4 ) has equal zeroes is
This question has multiple correct options
A .4
B . 2
( c .-4 )
D. –
10
329( frac{1-frac{9}{y^{2}}}{1-frac{3}{y}}-frac{3}{y}, ) where ( (y neq 0)= )
A. ( frac{y-3}{y} )
в. ( frac{y+3}{y} )
( c cdot 3 )
D.
E ( .3 y-1 )
10
330Solve :
( sqrt{2} x^{2}-sqrt{3} x-3 sqrt{2} )
10
331Factories:
( x^{2}+6 x+9 )
10
332If one of the zeroes of the polynomial ( boldsymbol{f}(boldsymbol{z})=boldsymbol{p}^{2} boldsymbol{z}^{2}+boldsymbol{8} boldsymbol{z}+boldsymbol{1} boldsymbol{6} ) is reciprocal of
the other, then the value of ( p ) is:
( A ldots pm 4 )
B. – 5
( c cdot 6 )
D. –
10
333If the sum of the roots of the equation ( x^{2}-x=k(2 x-1) ) is zero, find ( k )10
334If the equation ( x^{2}+b x+c=0 ) and
( boldsymbol{x}^{2}+boldsymbol{c} boldsymbol{x}+boldsymbol{b}=mathbf{0},(boldsymbol{b} neq boldsymbol{c}) ) have a
common root then
A. ( b+c=0 )
B. ( b+c=1 )
c. ( b+c+1=0 )
D. None of these
10
335Number of solutions of the equation ( (sqrt{3}+1)^{2 x}+(sqrt{3}-1)^{2 x}=2^{3 x} ) is10
336The roots of ( a^{2} x^{2}+a b x=b^{2}, a neq )
( mathbf{0}, boldsymbol{b} neq mathbf{0} ) are:
A. Equal
B. Non- real
c. Unequal
D. None of these
10
33717. Solve for x; (5+276)+2-3 +(5-216)*2-3 = 10
(1985 – 5 Marks)
10
338Classify the following polynomials as linear, quadratic, cubic and biquadratic polynomials:
( x+x^{2}-4 )
10
339If Sum of two numbers ( =-21 ) and
Product ( =-100 )
Then find the two numbers
10
340State whether the given algebraic expressions are polynomials? Justify. ( x^{2}+7 x+9 )10
341If ( a>0, ) then the expression ( a x^{2}+ )
( b x+c ) is positive for all values of ( x )
provided
A ( . b^{2}-4 a c>0 )
В. ( b^{2}-4 a c<0 )
( mathbf{c} cdot b^{2}-4 a c=0 )
D. ( b^{2}-a c<0 )
10
342The roots of the equation ( a x^{2}+b x+ )
( c=0 ) will be imaginary if
A. ( a>0, b=0, c0, b=0, c>0 )
c. ( a=0, b>0, c>0 )
D. ( a>0, b>0, c=0 )
10
343State true or false:
( x^{2}-5 x+6 ) cannot be written as a
product of two linear factors.
A . True
B. False
10
344The angry Arjun carried some arrows for fighting with Bheeshm. With half the arrows, he cut down the arrows thrown
by Bheeshm on him and with six other
arrows he killed the rath driver of
Bheeshm. With one arrow each, he
knocked down respectively the rath, flag and the bow of Bheeshm. Finally, with one more than four times the square
root of arrows he laid Bheeshm
unconscious on an arrow bed. Find the
total number of arrows Arjun had.
10
345For what value of ( k ) will ( x^{2}- )
( (3 k-1) x+2 k^{2}+2 k=11 ) have equal
roots?
( mathbf{A} cdot 9,-5 )
В. -9,5
( c .9,5 )
D. -9,-5
10
346If the equation ( a x^{2}+b x+c=0 )
( a, b, c in R ) have non-real roots, then
This question has multiple correct options
A ( cdot c(a-b+c)>0 )
B. ( c(a+b+c)>0 )
c. ( c(4 a-2 b+c)>0 )
D. None of the above
10
347Which of the following is a quadratic
equation?
A ( cdot x^{frac{1}{2}}+2 x+3=0 )
B ( cdot(x-1)(x+4)=x^{2}+1 )
( mathbf{c} cdot x^{4}-x+5=0 )
D. ( (2 x+1)(3 x-4)=2 x^{2}+3 )
10
348Find the roots of the equation ( 2 x^{2}- ) ( boldsymbol{x}+frac{mathbf{1}}{mathbf{8}}=mathbf{0} )10
349If ( a^{2}-5 a-1=0 ) and ( a neq 0 ; ) find:
( (i) a-frac{1}{a} )
( (mathrm{ii}) boldsymbol{a}+frac{mathbf{1}}{boldsymbol{a}} )
10
350Find the value of ( mu ) for which one root of
the quadratic equation ( mu x^{2}-14 x+ )
( 8=0 ) in 6 times the other.
10
351Which of the following is not a
quadratic equation?
A ( cdot 2(x-1)^{2}=4 x^{2}-2 x+1 )
B. ( left(x^{2}+1right)^{2}=x^{2}+3 x+9 )
( mathbf{C} cdotleft(x^{2}+2 xright)^{2}=x^{4}+3+4 x^{3} )
D ( cdot x^{2}+9=3 x^{2}-5 x )
10
352What is a Quadratic Equation?10
353Find a quadratic equation whose roots
( operatorname{are} alpha, beta ) such that ( alpha+beta=3 ) and ( alpha^{3}+ )
( boldsymbol{beta}^{mathbf{3}}=mathbf{9} )
10
354For the expression ( a x^{2}+7 x+2 ) to be
quadratic, the necessary condition is
( mathbf{A} cdot a=0 )
B. ( a neq 0 )
( ^{c} cdot_{a}>frac{7}{2} )
D. ( a<-1 )
10
355The values of ( k, ) so that the equations
( 2 x^{2}+k x-5=0 ) and ( x^{2}-3 x-4=0 )
have one root in common, are
A ( cdot_{3, frac{27}{2}} )
в. ( 9, frac{27}{4} )
c. ( _{-3, frac{-27}{4}} )
D. ( -3, frac{4}{27} )
10
356The given equation ( (x+1)^{2}=2(x-3) )
is
A . linear
B. quadratic
c. cubic
D. none of these
10
357Find the value of ( s, ) if ( 3 s^{2}+8 s+3 )10
358Find the equation whose roots are the
reciprocals of the roots of ( 3 x^{2}-5 x+ )
( mathbf{7}=mathbf{0} )
A ( cdot 7 x^{2}-5 x+3=0 )
B . ( 7 x^{2}+5 x+3=0 )
c. ( 4 x^{2}-5 x+3=0 )
D. ( 7 x^{2}-5 x+7=0 )
10
359If ( left(2 x^{2}-3 x+1right)left(2 x^{2}+5 x+1right)=9 x^{2} )
A. For real root
B. Two real and two imaginary root
c. Four imaginary roots
D. None of the above
10
3607.
The solution of the equation
5x^2(2x– 7) = 2(3x-1) +
10
361If 1 lies between the roots of the
equation ( y^{2}-m y+1=0 ) and ( [x] ) is
the GIF function,
then the value of ( left[left(frac{4|x|}{|x|^{2}+16}right)^{m}right], ) is
( mathbf{A} cdot mathbf{0} )
B.
( c cdot 2 )
D. None of the above
10
362Solve:
( x+frac{1}{x}=25 frac{1}{25} )
10
363Choose best possible option. ( left(x+frac{1}{2}right)left(frac{3 x}{2}+1right)= )
( frac{6}{2}(x-1)(x-2) ) is quadratic.
A. Yes
B. No
c. Complex equation
D. None
10
364Solve the equation ( x^{2}-2 b x+left(b^{2}-right. )
( left.boldsymbol{a}^{2}right)=mathbf{0} )
10
36562. The speed of the current is 5 km
hour. A motorboat goes 10 km
upstream and back again to the
starting point in 50 minutes. The
speed, in km/hour, of the mo-
torboat in still water is
(1) 20 (2) 26
(3) 25
(4) 28
10
366Check whether ( 5-6 x=frac{2}{5} x^{2} ) is
a quadratic equation.
10
367Solve the following by using the method of completing square. ( 6 x^{2}-11 x+3=0 )10
368Which of the following equations have no real roots ?
A ( cdot x^{2}-2 sqrt{3}+5=0 )
B ( cdot 2 x^{2}+6 sqrt{2} x+9=0 )
c. ( x^{2}-2 sqrt{3}-5=0 )
D ( cdot 2 x^{2}-6 sqrt{2} x-9=0 )
10
369The given quadratic equation have real roots and the roots are ( -2 sqrt{3}, frac{-sqrt{3}}{2} ) ( mathbf{2} boldsymbol{x}^{2}+mathbf{5} sqrt{mathbf{3}} boldsymbol{x}+mathbf{6}=mathbf{0} )
A. True
B. False
10
37015. If one root of the quadratic equation ax2 + bx+c=0 is
equal to the n-th power of the other, then show that
(ac”)”+1 +(a” c)2+1 +b=0
(1983 – 2 Marks)
10
371Solve: ( x^{2}+y^{2}-4 x-4 y+8=0 )10
372The nature of the roots of the equation ( x^{2}-5 x+7=0 ) is
A. No real roots
B. 1 real root and 1 imaginary
c. Real and unequal
D. Real and equal
10
373Two types of boxes ( A, B ) are to be
placed in a truck having capacity of 10
tons. When 150 boxes of type ( A ) and 100 boxes of type ( B ) are loaded in the truck, it weighs 10 tons. But when 260 boxes
of type ( A ) are loaded in the truck, it can
still accommodate 40 boxes of type ( B )
so that it is fully loaded. Find the weight of each type of box.
10
374If the quadratic equation ( x^{2}+b x+ )
( mathbf{7 2}=mathbf{0} ) has two distinct integer roots,
then the number of all possible values of bis
A . 12
B. 9
c. 15
D. 18
10
375The set of values of ( p ) for which the roots
of the equation ( 3 x^{2}+2 x+p(p-1)= )
0 are of opposite sign is
( A cdot(-infty, 0) )
B. (0,1)
c. ( (1, infty) )
D. ( (0, infty) )
10
376If sec ( alpha ) and ( csc alpha ) are the roots of ( x^{2}- )
( boldsymbol{p} boldsymbol{x}+boldsymbol{q}=boldsymbol{0} ) then
A ( cdot p^{2}=q(q-2) )
B . ( p^{2}=q(q+2) )
c. ( p^{2}+q^{2}=2 q )
D・ ( p^{2}+q^{2}=1 )
10
377Assertion
If the roots of the equations ( x^{2}-b x+ )
( c=0 ) and ( x^{2}-c x+b=0 ) differ by the
same quantity, then ( b+c ) is equal to
-4
Reason
If ( alpha, beta ) are the roots of the equation ( A x^{2}+B x+C=0, ) then ( alpha-beta= )
( frac{sqrt{boldsymbol{B}^{2}-boldsymbol{4} boldsymbol{A} boldsymbol{C}}}{boldsymbol{A}} )
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct
10
378The length of a rectangular verandah is
( 3 m ) more than its breadth. The
numerical value of its area is equal to
the numerical value of its
perimeter. Taking ( x ) as the breadth of
the verandah, write an equation in ( x )
that represents the above statement.
A ( cdot x^{2}-x-6=0 )
B. ( x^{2}-x+6=0 )
c. ( x^{2}-x+5=0 )
D. ( x^{2}-x-5=0 )
10
379Find the number of all real solution to
the quadratic equation ( x^{2}+2 x=-1 )
10
380Which of the following steps should be
followed to convert a given word problem into a Quadratic Equation?
A. Represent the unknown quantity/ies with variables ( (x ) y etc.
B. Express the information of the problem mathematically in the form of an equation.
c. check if the equation formed is in one variable and the degree of the equation is 2
D. All of the above
10
38116. Find all real values of x which satisfy x2-3x+2> 0 and
x-2x-450
(1983 – 2 Marks)
10
382The expression ( 21 x^{2}+a x+21 ) is to be
factored into two linear prime binomial factors with integer coefficients. This
can be done if a is:
A. odd number
B. zero
c. even number
D. None
10
383Before Robert Norman worked on ‘Dip and Field Concept’, his predecessor thought that the tendency of the magnetic needle to swing towards the
poles was due to a point attractive. However, Norman showed with the help of experiment that nothing like point attractive exists. Instead, he argued that magnetic power lies is lodestone. Which one of the following is the problem on which Norman and others
worked?
A. Existence of point attractive
B. Magnetic power in lodestone
c. Magnetic power in needle
D. swinging of magnetic needle
10
384Find the value of x for which the
expression 2 – 3x – 4×2 has the
greatest value.
(1)
16
10
385Is the following equation a quadratic equation? ( (x+2)^{3}=x^{3}-4 )
A. Yes
B. No
c. Ambiguous
D. Data insufficient
10
386Check whether the following are Quadratic equations
( (x+2)^{3}=2 xleft(x^{2}-1right) )
10
387The sum of all real values of ( x ) satisfying the equation ( left(x^{2}-5 x+5right)^{x^{2}+4 x-60}=1 )
is?
10
388If ( a^{2}-a b=0, ) which of the following is
the correct conclusion?
( mathbf{A} cdot a=0 )
B . ( a=b )
( mathbf{c} cdot a^{2}=b )
D. either ( a=0 ) or ( a=b )
10
389Using the identity ( a^{2}-b^{2}= )
( (a+b)(a-b) ) solve ( left(7 frac{3}{4}right)^{2}-left(2 frac{1}{4}right)^{2} )
10
390The product of 2 consecutive integers is 20 find them10
39163. The current of a stream runs
at the rate of 4 km an hour. A
boat goes 6 km and comes back
to the starting point in 2
hours. The speed of the boat
in still water is
(1) 6 km/hour
(2) 8 km/hour
(3) 7.5 km/hour
(4) 6-8 km/hour
10
392f ( p=-2, ) find the value of:
( -3 p^{2}+4 p+7 )
10
393Find the root of the quadratic equation
( x^{2}+2 sqrt{2 x}+6=0 ) by using the
quadratic formula
A . ( x=sqrt{2} pm 2 i )
B. ( x=-sqrt{2} pm 2 i )
c. ( x=-sqrt{4} pm 2 i )
D. ( x=-sqrt{2} pm 4 i )
10
394The expression ( frac{5-x}{x^{2}-x-20} ) when simplified equals
A ( cdot frac{1}{(x+4)} )
в. ( frac{1}{(x-4)} )
c. ( -frac{1}{(x+4)} )
D. ( frac{1}{(x-5)} )
10
395For what values of ( m in R, ) both roots of
the equation ( x^{2}-6 m x+9 m^{2}- )
( 2 m+2=0 ) exceed ( 3 ? )
B. ( left(frac{11}{9}, inftyright) )
c. ( [1, infty] )
D. ( [0, infty] )
10
396If ( x^{4}+frac{1}{x^{4}}=119, ) then the value of ( x- )
( frac{1}{-} ) is
( x )
( A cdot 6 )
B. 12
c. 11
D.
10
397If the sum of the roots of the quadratic
equation ( a x^{2}+b x+c=0 ) is equal to
the sum of the square of their reciprocals, then ( frac{a}{c}, frac{b}{a} ) and ( frac{c}{b} ) are in
A . GP
в. нР
c. АGР
D. AP
10
398Check whether the following are
Quadratic equations
( x^{2}+3 x+1=(x-2)^{2} )
10
399Greatest ratio of roots of ( 4 x^{2}-2left(a^{2}+right. )
( left.b^{2}right) x+a^{2} b^{2}=0 ) if ( a=2 b )
10
400Find the roots of the equation ( 2 x^{2}+ )
( x-6=0 ) by factorisation.
10
401The number of roots of the equation ( 2^{x}+2^{x-1}+2^{x-2}=7^{x}+7^{x-1}+7^{x-2} )
is-
10
402Solve:
( frac{2 x-1}{x+4}-2 x-5 x+3=0 )
10
403Find the value of ( k ) for which the
equation ( 3 x^{2}-6 x+k=0 ) has distinct
and real root.
10
404Solve ( boldsymbol{x}+mathbf{2}+boldsymbol{y}+mathbf{3}+ )
( sqrt{(x+2)(y+3)}=39 )
( (x+2)^{2}+(y+3)^{2}+(x+2)(y+ )
3)( =741 )
10
405A quadratic equation in ( x ) is ( a x^{2}+ )
( boldsymbol{b} boldsymbol{x}+boldsymbol{c}=mathbf{0}, ) where ( boldsymbol{a}, boldsymbol{b}, boldsymbol{c} ) are real
numbers and the other condition is
( mathbf{A} cdot a neq 0 )
в. ( b neq 0 )
c. ( c neq 0 )
( mathbf{D} cdot b=0 )
10
406Find the quadratic function ( boldsymbol{f}(boldsymbol{x}) boldsymbol{i} boldsymbol{f} boldsymbol{f}(boldsymbol{0})=mathbf{1}, boldsymbol{f}(1)=mathbf{0}, boldsymbol{a} boldsymbol{n} boldsymbol{d} boldsymbol{f}(boldsymbol{3})= )
( mathbf{5} )
10
407Find the value of discriminant for
( sqrt{3} x^{2}+2 sqrt{2} x-2 sqrt{3}=0 )
10
408Which of the following is a quadratic polynomial in one variable?
A. ( sqrt{2 x^{3}}+5 )
.
B. ( 2 x^{2}+2 x^{-2} )
c. ( x^{2} )
D. ( 2 x^{2}+y^{2} )
10
409Ifa, ß are the roots of x2 + px +q=0 and y, 8 are the roots
of r+rx+s=0, evaluate (a-ya-8)(-y)
(B-8) in terms of p, q, r and s.
Deduce the condition that the equations have a common
(1979)
root.
10
410Equation of the tangent at (4,4) on ( x^{2}= )
4y is
A. ( 2 x+y+4=0 )
В. ( 2 x-y-4=0 )
c. ( 2 x+y-12=0 )
D. ( 2 x+y+12=0 )
10
411Find the value(s) of ( k ) for which the
equation ( boldsymbol{x}^{2}+mathbf{5} boldsymbol{k} boldsymbol{x}+mathbf{1 6}=mathbf{0} ) has equal
roots.
10
41263. 11 (*+
+* +- 4 = 0.
then possible of x will be (x+0.
x# 1)
(1) 5485 2 515
(3 3445 (4) – 3415
10
413In the following, determine the value of
( k ) for which the given value is a solution
of the equation.
( mathbf{3} boldsymbol{x}^{2}+mathbf{2} boldsymbol{k} boldsymbol{x}-mathbf{3}=mathbf{0}, boldsymbol{x}=-frac{mathbf{1}}{mathbf{2}} )
10
414If the quadratic equation ( k x^{2}-2 k x+ )
( 6=0 ) has equal roots, then find the
value of ( k )
10
415The sum of the real roots of the
equation ( |boldsymbol{x}-mathbf{2}|^{2}+|boldsymbol{x}-mathbf{2}|-mathbf{2}=mathbf{0} )
( A cdot 2 )
B. 3
( c cdot 4 )
D.
10
416Divide 18 into 2 parts such that their product is 81
A. 9,-9
в. 3,27
c. ( 9, frac{1}{9} )
D. 9,9
10
417If ( boldsymbol{A}=boldsymbol{x}^{2}+boldsymbol{x}+mathbf{1}, boldsymbol{B}=boldsymbol{x}^{2}-boldsymbol{x}+mathbf{1} )
then ( boldsymbol{A}-mathbf{2} boldsymbol{B} )
10
4187.
Find all integers x for which
(5x-1)<(x+1)2 < (Tx-3).
10
419Discriminant of the equation ( -3 x^{2}+ )
( 2 x-8=0 ) is
A . -92
B. -29
c. 39
D. 49
10
420Find the value of ( k ) for which the
quadratic equation ( (k-2) x^{2}+ )
( 2(2 k-3) x+5 k-6=0 ) has equal
roots
( A )
B. 3
c. A and B both
D. none of these
10
421If ( alpha ) and ( beta ) are zeroes of the polynomial ( 2 x^{2}+3 x+7 . ) Find a quadratic
polynomial whose zeroes are ( frac{1}{alpha^{2}} & frac{1}{beta^{2}} )
A ( cdot 49 x^{2}+18 x+4 )
B . ( 49 x^{2}-18 x+4 )
c. ( 49 x^{2}-23 x-4 )
D. ( 49 x^{2}-21 x+4 )
10
422Determine the nature of roots of the
following quadratic equation:
( 2 x^{2}+5 x+5=0 )
10
423The solution of the equation ( boldsymbol{x}+frac{mathbf{1}}{boldsymbol{x}}=mathbf{2} )
will be
A .2,-1
в. ( _{0,-1,-frac{1}{5}} )
( mathrm{c} cdot_{-1,-frac{1}{5}} )
D. None of these
10
424Negetive of Discriminant of the following quadratic equation is :
( x^{2}-x+1=0 )
10
425If one root of ( x^{2}+a x+8=0 ) is 4 and
the equation ( x^{2}+a x+b=0 ) has equal
roots, then ( b= )
A . 7
B. 9
( c .1 )
D. 3
10
426Which is a quadratic equation?
A ( cdot x+frac{1}{x}=2 )
B . ( x^{2}+1=(x+3)^{2} )
c. ( x(x+2) )
D. ( _{x+frac{1}{x}} )
10
427If ( n ) is a positive integer and ( n in[5,100] )
then the number of integral roots of the equation ( x^{2}+2 x-n=0 ) are
A . 4
B. 6
c. 8
D. 10
10
428If the equation ( 2 x^{2}-6 x+p=0 ) has
real and different roots, then the values
of ( p ) are given by
( ^{A} cdot_{p}frac{9}{2}} )
( mathrm{D} cdot_{p} geq frac{9}{2} )
10
429Let ( a, b, c ) be the sides of a triangle. No
two of them are equal and ( lambda epsilon R ) If the
roots of the equation ( x^{2}+2(a+b+ )
( c) x+3 lambda(a b+b c+c a)=0 ) are real
then.
10
430Check whether the following is a quadratic equation or not
( (x+1)^{2}=2(x-3) )
10
431If both roots of the equation ( a x^{2}+ ) ( 2 x a+1+a^{2}-16=0 ) are opposite in
( operatorname{sign}, ) then the range of ( a ) is
( A cdot(-infty,-4) cup(4, infty) )
B . (-4,4)
( mathbf{c} cdot(-infty,-4) cup(0,4) )
D ( cdot(0,4) )
10
432The trinomial ( a x^{2}+b x+c ) has no real
roots, ( a+b+c<0 . ) Find the sign of
the number ( c )
10
433The sign of the quadratic polynomial
( a x^{2}+b x+c ) is always positive, if?
( mathbf{A} cdot ) a is positive and ( b^{2}-4 a c leq 0 )
B. a is positive and ( b^{2}-4 a geq 0 )
( mathrm{C} cdot ) a can be any real number and ( b^{2}-4 a c leq 0 )
D. a can be any real number and ( b^{2}-4 a c geq 0 )
10
434The roots of ( a x^{2}+b x+c=0, ) where
( a neq 0, b, c epsilon R ) are non real complex and
( a+c2 b )
B . ( 4 a+c<2 b )
c. ( 4 a+c=2 b )
D. None of these
10
435( boldsymbol{x}^{2}-(boldsymbol{m}-mathbf{3}) boldsymbol{x}+boldsymbol{m}=mathbf{0}(boldsymbol{m} in boldsymbol{R}) ) be a
quadratic equation. Find the value of ( boldsymbol{m} )
for which both the roots are equal:
A ( cdot{1,9} )
B.
( c .3 )
D. {4,11}
10
436The value of ( k, ) of the roots of the
equation ( 2 k x^{2}+2 k x+2=0 ) are
equal is
( A cdot frac{4}{5} )
B. 4
c. 1
D.
10
437( frac{x-a}{x-b}+frac{x-b}{x-a}= )10
438The given quadratic equations have real roots and roots are Real and equal, ( sqrt{frac{3}{2}} )
( mathbf{2} boldsymbol{x}^{2}-mathbf{2} sqrt{mathbf{6} boldsymbol{x}}+mathbf{3}=mathbf{0} )
A. True
B. False
10
439If ( boldsymbol{alpha}, boldsymbol{beta} in boldsymbol{C} ) are the distinct roots, of the
equation ( x^{2}-x+1=0, ) then ( alpha^{101}+ )
( beta^{107} ) is equal to
A .
B. 2
( c cdot-1 )
D.
10
440Identify which of the following is/are
a quadratic polynomial function:
This question has multiple correct options
( mathbf{A} cdot f(x)=(x+1)^{3}-(x+2)^{3} )
( g(x)=left{begin{array}{cc}frac{x^{4}}{x^{2}} & text { if } x neq 0 \ 0 & text { if } x=0end{array}right. )
C ( cdot h(x)=(x+1)^{2}-(x+2)^{2} )
D. All of these
10
441Solve the equation:
( 4 x^{2}-4 p x+left(p^{2}-q^{2}right)=0 )
10
442f ( x=3 t, y=1 / 2(t+1), ) then the value
of ( t ) for which ( x=2 y ) is
( A cdot 1 )
B. ( 1 / 2 )
( c .-1 )
D. ( 2 / 3 )
10
443Is the given equation quadratic? Enter 1 for True and 0 for False.
( boldsymbol{n}-mathbf{3}=mathbf{4} boldsymbol{n}^{2} )
10
444If the roots of the equation ( frac{alpha}{x-alpha}+ ) ( frac{beta}{boldsymbol{x}-beta}=1 ) be equal in magnitude but
opposite in ( operatorname{sign}, ) then ( alpha+beta ) is equal to:
A.
B. 1
( c cdot 2 )
D.
10
445Decide whether ( m^{2}+m+2=4 m ) is a
quadratic equation
10
446The number of solutions of the
equation, ( 2{x}^{2}+5{x}-3=0 ) is
A. No solution
B.
( c cdot 2 )
D. Infinite
10
447The number of quadratic equation which are unchanged by squaring their roots is10
448( boldsymbol{x}^{2}-(boldsymbol{m}-mathbf{3}) boldsymbol{x}+boldsymbol{m}=mathbf{0}(boldsymbol{m} in boldsymbol{R}) ) be a
quadratic equation. Find the value of ( boldsymbol{m} )
for which, both the roots lie in the
interval of (1,2)
A. ( (10, infty) )
)
в. ( (-infty, 0) )
( c cdot(-infty, infty) )
D. None of the above
10

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