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Quadratic Equation — NDA Mathematics PYQs

157 previous year questions from Quadratic Equation with answers and solutions. Numbered list, year tags, and one-tap solutions — built for serious JEE / NEET practice.

157 questionsMathematicsSolutions on every page
1

For a given k , what is the minimum value of x^2+kx+k^2 ?

NDA 2026 Solution View → 2

If the highest degree coefficient is equal to 1 , then what is the total number of quadratic equations which are unchanged on squaring their roots ?

NDA 2026 Solution View → 3

Let and be the roots of the quadratic equation x^2-2bx+c^2=0 where b , c are positive real numbers. Let A be the arithmetic mean of and ; and G be the geometric mean of and . What

NDA 2026 Solution View → 4

Consider the following statements : I. x +x+1=0 has two irrational roots. II. 5 x -x-4=0 has two rational roots. Which of the statements given above is/are correct ?

NDA 2026 Solution View → 5

For the following two (02) items: Let f(x) = ax^2 + bx + c be a quadratic polynomial such that f(1) = f(4) = 2 . Further, 2 is a root of f(x) = 0 . What is (a + b + c) equal to?

NDA 2025 Solution View → 6

For the following two (02) items: Let and be the roots of the quadratic equation x^2 + ( _ 0.5 (a^2))x + ( _ 0.5 (a^2))^4 = 0 , where a^2 1 and _ 0.5 (a^2) > 0 . Further, ^2 = ( _

NDA 2025 Solution View → 7

For the following two (02) items: Let f(x) = ax^2 + bx + c be a quadratic polynomial such that f(1) = f(4) = 2 . Further, 2 is a root of f(x) = 0 . What is the other root of f(x) =

NDA 2025 Solution View → 8

If one root of the equation x^2 - kx + k = 0 exceeds the other by 2 3 , then which one of the following is a value of k ?

NDA 2025 Solution View → 9

For the following two (02) items: Let and be the roots of the quadratic equation x^2 + ( _ 0.5 (a^2))x + ( _ 0.5 (a^2))^4 = 0 , where a^2 1 and _ 0.5 (a^2) > 0 . Further, ^2 = ( _

NDA 2025 Solution View → 10

If x = (1111)₂ , y = (1001)₂ and z = (110)₂ , then what is x^3 - y^3 - z^3 - 3xyz equal to?

NDA 2025 Solution View → 11

If x^2 - x + 1 = 0 , then what is (x - 1 x )^2 + (x - 1 x )^4 + (x - 1 x )^8 equal to?

NDA 2025 Solution View → 12

If x + 5 y = 4 and y + 5 x = -4 , then what is (x + y) equal to?

NDA 2025 Solution View → 13

For the following two (02) items: Consider the equation abx^2 + bcx + ca = cax^2 + abx + bc . If the roots of the equation are equal, then a , b , c are in

NDA 2025 Solution View → 14

For the following two (02) items: Consider the equation abx^2 + bcx + ca = cax^2 + abx + bc . If the roots of the equation are equal, then which one of the following is correct?

NDA 2025 Solution View → 15

If n is a root of the equation x^2+p x+m=0 and m is a root of the equation x^2+p x+n=0 , where m n , then what is the value of p+m+n ?

NDA 2024 Solution View → 16

The roots of the equation 7 x^2-6 x+1=0 are and , where 2 and 2 are the angles of a triangle. Which one of the following is correct?

NDA 2024 Solution View → 17

Paragraph: The roots of the quadratic equation a^2 (b^2-c^2 ) x^2+b^2 (c^2-a^2 ) x+c^2 (a^2-b^2 )=0 are equal (a^2 b^2 c^2 ) . Question: Which one of the following statements is co

NDA 2024 Solution View → 18

What is the number of real roots of the equation (x-1)^2+(x-3)^2+(x-5)^2=0 ?

NDA 2024 Solution View → 19

If f(x)=9 x-8 x such that g(x)=f(x)-1 , then which one of the following is correct?

NDA 2024 Solution View → 20

Paragraph: The roots of the quadratic equation a^2 (b^2-c^2 ) x^2+b^2 (c^2-a^2 ) x+c^2 (a^2-b^2 )=0 are equal (a^2 b^2 c^2 ) . Question: Which one of the following is a root of the

NDA 2024 Solution View → 21

If - 2 and 3 are roots of the equation a₀+a₁ x+a₂ x^2+a₃ x^3+x^4=0 where a₀, a₁, a₂, a₃ are integers, then which one of the following is correct?

NDA 2024 Solution View → 22

If a, b and c(a 0, c 0) are in GP, then consider the following in respect of the equation a x^2+b x+c=0: 1. The equation has imaginary roots. 2. The ratio of the roots of the equat

NDA 2024 Solution View → 23

Under which one of the following conditions does the equation ( -1) x^2+( ) x+ =0 in x have a real root for [0, ] ?

NDA 2024 Solution View → 24

If x^2+m x+n is an integer for all integral values of x , then which of the following is/are correct? 1. m must be an integer 2. n must be an integer Select the correct answer usin

NDA 2024 Solution View → 25

Consider the equation (1-x)^4+(5-x)^4=82 What is the sum of all the roots of the equation?

NDA 2023 Solution View → 26

A quadratic equation is given by (a+b) x^2-(a+b+c) x+k=0 , where a, b, c are real. If k= c 2 ,(c 0) , then the roots of the equation are:

NDA 2023 Solution View → 27

For how many integral values of k , the equation x^2-4 x+k=0 , where k is an integer, has real roots and both of them lie in the interval (0,5) ?

NDA 2023 Solution View → 28

If 2-i 3 where i= -1 is a root of the equation x^2+a x+b=0 , then what is the value of (a+b) ?

NDA 2023 Solution View → 29

and are distinct real roots of the quadratic equation x ^2+ ax + b =0 . Which of the following statements is/are sufficient to find ? 1. + =0, ^2+ ^2=2 2. ^2=-1, a=0 Select the cor

NDA 2023 Solution View → 30

Paragraph: Consider the following for the next two (02) items that follow: A quadratic equation is given by (3+2 2 ) x^2-(4+2 3 ) x+(8+4 3 )=0 Question: What is the HM of the roots

NDA 2023 Solution View → 31

Paragraph: Consider the following for the next two (02) items that follow: A quadratic equation is given by (3+2 2 ) x^2-(4+2 3 ) x+(8+4 3 )=0 Question: What is the GM of the root

NDA 2023 Solution View → 32

Consider the equation (1-x)^4+(5-x)^4=82 What is the number of real roots of the equation?

NDA 2023 Solution View → 33

A quadratic equation is given by (a+b) x^2-(a+b+c) x+k=0 , where a, b, c are real. If k = c, then the roots of the equation are:

NDA 2023 Solution View → 34

Let p, q(p q) be the roots of the quadratic equation x^2+b x+c=0 where c 0 . If p^2+q^2-11 p q=0 , then what is p-q equal to?

NDA 2022 Solution View → 35

Let and ( ) be the roots of the equation x^2-8 x+q=0 . If ^2- ^2=16 , then what is the value of q ?

NDA 2022 Solution View → 36

Let and be the roots of the equation x^2+p x+q=0 . If ^3 and ^3 are the roots of the equation x^2+m x+n=0 , then what is the value of m+n ?

NDA 2022 Solution View → 37

For how many quadratic equations, the sum of roots is equal to the product of roots?

NDA 2022 Solution View → 38

If the roots of the equation x^2-a x-b x-c x+b c+c a=0 are equal, then which one of the following is correct?

NDA 2022 Solution View → 39

Let and be the roots of the equation x^2-a x-b x+a b-c=0 . What is the quadratic equation whose roots are a and b ?

NDA 2022 Solution View → 40

The quadratic equation 3 x^2- (k^2+5 k ) x+3 k^2-5 k=0 has real roots of equal magnitude and opposite sign. Which one of the following is correct?

NDA 2021 Solution View → 41

If the roots of the equation 4 x^2-(5 k+1) x+5 k=0 differ by unity, then which one of the following is a possible value of k ?

NDA 2021 Solution View → 42

If p and q are the non-zero roots of the equation x^2+p x+q=0 , then how many possible values can q have?

NDA 2021 Solution View → 43

If and are the roots of the equation a x^2+b x+c=0 , then which one of the following is correct?

NDA 2021 Solution View → 44

What is the probability that the roots of the equation x^2+x+n=0 are real, where n N and n 4 ?

NDA 2021 Solution View → 45

If the roots of the quadratic equation x^2+2 x+k=0 are real, then

NDA 2021 Solution View → 46

If and are the roots of the equation 4 x^2+2 x-1=0 , then which one of the following is correct?

NDA 2021 Solution View → 47

If one root of 5 x^2+26 x+k=0 is reciprocal of the other, then what is the value of k ?

NDA 2021 Solution View → 48

If x+y=20 and P=x y , then what is the maximum value of P ?

NDA 2021 Solution View → 49

If k is one of the roots of the equation x(x+1)+1=0 , then what is its other root?

NDA 2021 Solution View → 50

Consider all the real roots of the equation x^4-10 x^2+9=0 . What is the sum of the absolute values of the roots?

NDA 2021 Solution View → 51

The roots and of a quadratic equation, satisfy the relations + = ^2+ ^2 and = ^2 ^2 . What is the number of such quadratic equations?

NDA 2020 Solution View → 52

If f(x)=3 x^2-5 x+p and f(0) and f(1) are opposite in sign, then which of the following is correct?

NDA 2020 Solution View → 53

If and are the roots of the equation x^2-3 x+2=0 , then what is ( + ) equal to ?

NDA 2020 Solution View → 54

If both p and q belong to the set (1,2,3,4) , then how many equations of the form p x^2+q x+1=0 will have real roots?

NDA 2019 Solution View → 55

What is the value of k for which the sum of the squares of the roots of 2 x^2-2(k-2) x-(k+1)=0 is minimum?

NDA 2019 Solution View → 56

If the roots of the equation a(b-c) x^2+b(c-a) x+c(a-b)=0 are equal, then which one of the following is correct?

NDA 2019 Solution View → 57

Under which one of the following conditions will the quadratic equation x^2+m x+2=0 always have real roots?

NDA 2019 Solution View → 58

How many real roots does the equation x^3+3|x|+2=0 have?

NDA 2019 Solution View → 59

If and are the roots of x^2+x+1=0 , then what is _ j=0 ^3 ( ^j+ ^j ) equal to?

NDA 2019 Solution View → 60

Consider the following statements in respect to the quadratic equation 4(x-p)(x-q)-r^2=0 where p, q and r are real numbers : 1. The roots are real 2. The roots are equal if p=q and

NDA 2019 Solution View → 61

Which one of the following is the second degree polynomial function f(x) where f(0)=5, f(-1)=10 and f(1)=6 ?

NDA 2019 Solution View → 62

If p and q are the roots of the equation x^2-30 x+221=0 , what is the value of p^3+q^3 ?

NDA 2019 Solution View → 63

Paragraph: Let f(x)=x^2+2 x-5 and g(x)=5 x+30 Question: What are the roots of the equation g[f(x)]=0 ?

NDA 2019 Solution View → 64

What are the roots of the equation |x^2-x-6 |=x+2 ?

NDA 2019 Solution View → 65

The equation px ^2+ qx + r =0 (where p , q , r , all are positive) has distinct real roots a and b . Which one of the following is correct?

NDA 2019 Solution View → 66

If A= x Z: x^3-1=0 and B= x Z: x^2+x+ .1=0 , where Z is set of complex numbers, then what is A B equal to ?

NDA 2019 Solution View → 67

The number of real roots for the equation x^2+9|x|+20=0 is

NDA 2019 Solution View → 68

If the roots of the equation x^2+p x+q=0 are 19^ and 26^ , then which one of the following is correct ?

NDA 2019 Solution View → 69

If and (0 ) are the roots of the quadratic equation 4 x^2-3=0 , then what is the value of ?

NDA 2018 Solution View → 70

Suppose f(x) is such a quadrant expression that it is positive for all real x . If g(x)=f(x)+f^ (x)+f^ (x) , then for anyreal x . Then for any real x .

NDA 2018 Solution View → 71

The ration of roots of the equations a x^2+b x+c=0 and p x^2+q x+r=0 are equal. If D₁ and D₂ are respective discriminates, then what is D₁ D₂ equal to?

NDA 2018 Solution View → 72

The equation |1-x|+x^2=5 has

NDA 2018 Solution View → 73

If and ( 0) are the roots of the quadratic equation x^2+ x- =0 , then the quadratic expression -x^2+ x+ where x R has

NDA 2018 Solution View → 74

The roots of the equation (q-r) x^2+(r-p) x+(p-q)=0 are

NDA 2017 Solution View → 75

It is given that the roots of the equation x ^2-4 x - ₃ P =0 are real. For this, the minimum value of P is

NDA 2017 Solution View → 76

If and are the roots of the equation 3 x^2+2 x+1=0 , then the equation whose roots are + ⁻¹ and + ⁻¹ is

NDA 2017 Solution View → 77

If the difference between the roots of the equation x^2+k x+1=0 is strictly less than 5 , where | k | 2 , then k can be any element of the interval

NDA 2017 Solution View → 78

If and are the roots of the equation x^2+b x+c=0 with b 0 , then the value of ( + ) is

NDA 2017 Solution View → 79

If the roots of the equation x^2+p x+q=0 are in the same ratio as those of the equation x^2+l x+m=0 , then which one of the following is correct?

NDA 2017 Solution View → 80

The sum of the roots of the equation ax ^2+ x + c =0 (where a and c are non-zero) is equal to the sum of the reciprocals of their squares. Then a, ca ^2, c ^2 are in

NDA 2017 Solution View → 81

If the graph of a quadratic polynomial lies entirely above x -axis, then which one of the following is correct?

NDA 2017 Solution View → 82

The sum of the roots of the equation x^2+b x+c=0 (where b and c are non-zero) is equal to the sum of the reciprocals of their squares. Then 1 c , b , c b are in

NDA 2017 Solution View → 83

If S= (x: x^2+1=0, x . is real ) , then S is

NDA 2017 Solution View → 84

If c 0 and 4 a+c 2 b , then a x^2-b x+c=0 has a root in which one of the following intervals?

NDA 2016 Solution View → 85

If both the roots of the equation x^2-2 k x+k^2-4=0 lie between -3 and 5 , then which one of the following is correct?

NDA 2016 Solution View → 86

Paragraph: Let and be the roots of the equation x^2- (1-2 a^2 ) x+ (1-2 a^2 )=0 Question: Under what condition does the above equation have real roots?

NDA 2016 Solution View → 87

Paragraph: Let and be the roots of the equation x ^2- (1-2 a ^2 ) x + (1-2 a ^2 )=0 Question: Under what condition is 1 ^2 + 1 ^2 1 ?

NDA 2016 Solution View → 88

Paragraph: 2 x^2+3 x- -0 has roots -2 and while the equation x^2-3 mx +2 ~m ^2=0 has both roots positive, where 0 and 0 . Question: What is the value of ?

NDA 2016 Solution View → 89

Paragraph: 2 x^2+3 x- -0 has roots -2 and while the equation x^2-3 mx +2 ~m ^2=0 has both roots positive, where 0 and 0 . Question: If , 2,2 ~m are in GP, then what is the value of

NDA 2016 Solution View → 90

If x^2+p x+4 0 for all real values of x , then which one of the following is correct?

NDA 2016 Solution View → 91

Given that and are the roots of the equation x^2+b x+c=0 with b 0 . What is ( + ) equal to?

NDA 2016 Solution View → 92

Given that and are the roots of the equation x ^2+ bx + c =0 with b 0 . What is ( + ) equal to?

NDA 2016 Solution View → 93

Let and ( ) be the roots of the equation x ^2+ bx + c =0 , where b 0 and c 0 . Consider the following: 1. - 2. | | Which of the above is/are correct?

NDA 2016 Solution View → 94

Let and ( ) be the roots of the equation x ^2+ bx + c =0 , where b 0 and c 0 . Consider the following: 1. + + 0 2. ^2 + ^2 0 Which of the above is/are correct?

NDA 2016 Solution View → 95

If one root of the equation (1-m) x^2+1 x+1=0 is double the other and 1 is real, then what is the greatest value of m ?

NDA 2016 Solution View → 96

The number of real roots of the equation x^2-3|x|+2=0 is

NDA 2015 Solution View → 97

Consider the following statements in respect of the given equation : (x^2+2 )^2+8 x^2=6 x (x^2+2 ) 1. All the roots of the equation are complex. 2. The sum of all the roots of the

NDA 2015 Solution View → 98

If the roots of the equation x ^2- nx + m =0 differ by 1 , then

NDA 2015 Solution View → 99

If 2 p+3 q=18 and 4 p^2+4 p q-3 q^2-36=0 , then what is (2 p+q) equal to?

NDA 2015 Solution View → 100

In solving a problem that reduces to a quadratic equation, one student makes a mistake in the constant term and obtains 8 and 2 for roots. Another student makes a mistake only in t

NDA 2015 Solution View → 101

If the sum of the roots of the equation a x^2+b x+c=0 is equal to the sum of their squares, then

NDA 2015 Solution View → 102

The coefficient of x ⁹⁹ in the expansion of ( x -1)( x -2)( x -3) . . (x-100) is

NDA 2015 Solution View → 103

If m and n are the roots of the equation (x+p)(x+q)-k=0 , then the roots of the equation (x-m)(x-n)+k=0 are

NDA 2015 Solution View → 104

Let f(x)=a x^2+b x+c such that f(1)=f(-1) and a, b, c are in Arithmetic Progression. What is the value of b ?

NDA 2014 Solution View → 105

Every quadratic quation a x^2+b x+c=0 where a, b , c R , a 0 has

NDA 2014 Solution View → 106

If , are the roots of a x^2+b x+c=0 and +h , +h are the roots of p x^2+q x+r=0 , then what is h equal to?

NDA 2014 Solution View → 107

If and are the roots of the equation a x^2+b x+c=0 , where a 0 , then (a +b)(a +b) is equal to:

NDA 2014 Solution View → 108

The roots of the equation 2 a^2 x^2-2 a b x+b^2=0 when a 0 and b 0 are:

NDA 2014 Solution View → 109

The roots of the equation x^2-8 x+16=0

NDA 2013 Solution View → 110

What is the difference in the roots of the equation x^2-10 x+9=0 ?

NDA 2013 Solution View → 111

If , are the roots of the equation x^2+x+2=0 , then what is ¹⁰+ ¹⁰ ⁻¹⁰+ ⁻¹⁰ equal to?

NDA 2013 Solution View → 112

If 4^x-6.2^x+8=0 , then the values of x are

NDA 2013 Solution View → 113

If the roots of a quadratic equation a x^2+b x+c=0 are and , then the quadratic equation having roots ^2 and ^2 is

NDA 2013 Solution View → 114

If the roots of the equation 3 a x^2+2 b x+c=0 are in the ratio 2: 3 , then which one of the following is correct?

NDA 2013 Solution View → 115

If the sum of the roots of a quadratic equation is 3 and the product is 2 , then the equation is

NDA 2013 Solution View → 116

The area of a rectangle whose length is five more than twice its width is 75 square unit. The length is

NDA 2013 Solution View → 117

If , are the roots of the equation a x^2+b x+b=0 , then what is the value of + + b a ?

NDA 2013 Solution View → 118

The quadratic equation x^2+b x+4=0 will have real roots if

NDA 2013 Solution View → 119

How many real roots does the quadratic equation f(x)=x^2+3|x|+2=0 have?

NDA 2013 Solution View → 120

If a and b are rational and b is not perfect square, then the quadratic equation with rational coefficients whose one root is 3 a+ b is

NDA 2013 Solution View →
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