English Medium Class 10 - CBSE Important Questions

If 1 is a root of the quadratic equation 3x² + ax – 2 = 0 and the quadratic equation a(x² + 6x) – b = 0 has equal roots, find the value of b ?

Find the value(s) of k so that the quadratic equation 3x² − 2kx + 12 = 0 has equal roots ?

Find the roots of the equation  .`1/(2x-3)+1/(x+5)=1,x≠3/2,5`

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.

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 ______.

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 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 ______.

Find the value of ‘c’ for which the quadratic equation 

(c + 1) x² - 6(c + 1) x + 3(c + 9) = 0; c ≠ - 1

has real and equal roots.