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This mock test of Test: Nature Of Roots for Class 10 helps you for every Class 10 entrance exam.
This contains 25 Multiple Choice Questions for Class 10 Test: Nature Of Roots (mcq) to study with solutions a complete question bank.
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QUESTION: 1

The quadratic equation 2x^{2} – 3x + 5 = 0 has

Solution:

QUESTION: 2

The real roots of a quadratic equation ax^{2} + bx + c = 0 are given by

Solution:

When b^{2 }- 4ac=0 then we have the root as -b/2a.

When b^{2}-4ac < 0,then the root is a complex root ,since we have a negative number ,for which real square root is not possible.

When b^{2 }- 4ac > 0 then we have a square root of it and hence we have real roots. So the correct answer is b^{2 }- 4ac __>__ 0

QUESTION: 3

The solutions of the quadratic equation are

Solution:

QUESTION: 4

The value of b^{2} - 4ac for equation 3x^{2} - 7x - 2 = 0 is

Solution:

QUESTION: 5

Which of the following is not a quadratic equation ?

Solution:

QUESTION: 6

For what value(s) of k will the equation kx^{2}-5x+k = 0 have a repeated root?

Solution:

QUESTION: 7

A real number is said to be a root of ax^{2}+bx+c = 0

Solution:

QUESTION: 8

-3 is a root of the quadratic equation 2x^{2} +px – 15 = 0. For what value of q, the equation p(x^{2} + x ) + q = 0 has equal roots?

Solution:

QUESTION: 9

The roots of x^{2} – 8x + 12 = 0, are

Solution:

QUESTION: 10

If 1/2 is a root of the equation x^{2}+kx – (5/4) = 0, then the other root of the quadratic equation is

Solution:

QUESTION: 11

The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48. Find their present ages

Solution:

QUESTION: 12

The nature of the roots of following quadratic equation

Solution:

QUESTION: 13

If the equation px^{2} – 6x – 2 = 0 has real roots then, ________

Solution:

QUESTION: 14

The positive value of k, for which both equations: x^{2} + kx + 64 = 0 and x^{2} – 8x + k = 0 have real roots is_______

Solution:

QUESTION: 15

If one root of a Quadratic equation is m +, then the other root is

Solution:

In a quadratic equation with rational coefficients has an irrational root α + √β, then it has a conjugate root α - √β.

So if the root is m+ √n the other root will be m- √n

QUESTION: 16

If the value of the Discriminant function of a quadratic equation is D = 27, then its roots are

Solution:

QUESTION: 17

Comment on the nature of the roots of the equation 7x - 3x^{2} - 2 = 0

Solution:

QUESTION: 18

The roots of the equation x^{2} – 3x – m (m + 3) = 0, where m is a constant, are

Solution:

X^{2} - 3x - m(m+3) = 0

=> x^{2} + mx - (m+3)x- m(m+3) = 0

=> x(x+m) - (m+3)(x+m) = 0

=> (x+m) (x-m-3) = 0

x = - m and m+3

Roots are - m and m+3

QUESTION: 19

If the equation 9x^{2} – 6x + c = 0 has equal roots then, the value of c is

Solution:

QUESTION: 20

If -3 is a root of both the Quadratic equations 2×2 + px – 15 = 0, and p(x^{2} + x) + q = 0, then the value of q if the equation containing it has equal roots is

Solution:

QUESTION: 21

If a,b,c are real and b^{2}-4ac >0 then roots of equation are

Solution:

QUESTION: 22

The quadratic equation whose roots are real and equal is:

Solution:

QUESTION: 23

Which of the following equations has two distinct real roots?

Solution:

QUESTION: 24

If the equation 2x^{2} + 2(c - 20) x + (c - 20) = 0 has equal roots then, the value of c is

Solution:

QUESTION: 25

Which of the following is a solution of the quadratic equation x^{2} - b^{2} = a (2x - a)

Solution:

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