English Medium कक्षा १० - CBSE Important Questions for Mathematics

For what values of k, the roots of the equation x² + 4x +k = 0 are real? 

Find the value of k for which the roots of the equation 3x² -10x +k = 0 are reciprocal of each other.

Find the value(s) of k for which the pair of equations
kx +  2y = 3
3x + 6y = 10 has a unique solution.

Let ∆ ABC ∽ ∆ DEF and their areas be respectively, 64 cm² and 121 cm². If EF = 15⋅4 cm, find BC.

Write the discriminant of the quadratic equation (x + 5)² = 2 (5x − 3).

In the quadratic equation kx² − 6x − 1 = 0, determine the values of k for which the equation does not have any real root.

Values of k for which the quadratic equation 2x² – kx + k = 0 has equal roots is ______.

A natural number, when increased by 12, equals 160 times its reciprocal. Find the number.

Find the value of 𝑚 so that the quadratic equation 𝑚𝑥(5𝑥 − 6) = 0 has two equal roots.

Solve for x: 9x² – 6px + (p² – q²) = 0

Let p be a prime number. The quadratic equation having its roots as factors of p is ______.

Find the value of ‘k’ for which the quadratic equation 2kx² – 40x + 25 = 0 has real and equal roots.

Solve for x: `5/2 x^2 + 2/5 = 1 - 2x`.

Solve the equation: 3x² – 8x – 1 = 0 for x.

Find the value(s) of 'a' for which the quadratic equation x² – ax + 1 = 0 has real and equal roots.

If 'p' is a root of the quadratic equation x² – (p + q) x + k = 0, then the value of 'k' is ______.

If one root of the quadratic equation x² + 12x – k = 0 is thrice the other root, then find the value of k.

If x = 3 is one of the roots of the quadratic equation x² – 2kx – 6 = 0, then the value of k is ______.

The nature of roots of the quadratic equation 9x² – 6x – 2 = 0 is ______.

If the discriminant of the quadratic equation 3x² - 2x + c = 0 is 16, then the value of c is ______.