English Medium कक्षा १० - CBSE Important Questions

Solve the quadratic equation 2x² + ax − a² = 0 for x.

The numerator of a fraction is 3 less than its denominator. If 2 is added to both the numerator and the denominator, then the sum of the new fraction and original fraction is `29/20`. Find the original fraction.

Find the roots of the following quadratic equation by factorisation:

`sqrt2 x^2 +7x+ 5sqrt2 = 0`

Find the value of k for which the equation x² + k(2x + k − 1) + 2 = 0 has real and equal roots.

The sum of two natural numbers is 15 and the sum of their reciprocals is `3/10`. Find the numbers.

Solve for x:

4x² + 4bx − (a² − b²) = 0

A quadratic equation whose one root is 2 and the sum of whose roots is zero, is ______.

Solve the quadratic equation: `x^2 + 2sqrt(2)x - 6` = 0 for x.

Find the nature of the roots of the quadratic equation:

4x² – 5x – 1 = 0

If the sum of the roots of the quadratic equation ky² – 11y + (k – 23) = 0 is `13/21` more than the product of the roots, then find the value of k.

If x = –2 is the common solution of quadratic equations ax² + x – 3a = 0 and x² + bx + b = 0, then find the value of a²b.

If the quadratic equation ax² + bx + c = 0 has two real and equal roots, then 'c' is equal to ______.

Statement A (Assertion): If 5 + `sqrt(7)` is a root of a quadratic equation with rational co-efficients, then its other root is 5 – `sqrt(7)`.

Statement R (Reason): Surd roots of a quadratic equation with rational co-efficients occur in conjugate pairs.

If α and β are roots of the quadratic equation x² – 7x + 10 = 0, find the quadratic equation whose roots are α² and β².

Find the value of ‘p’ for which the quadratic equation px(x – 2) + 6 = 0 has two equal real roots.

Assertion (A): If one root of the quadratic equation 4x² – 10x + (k – 4) = 0 is reciprocal of the other, then value of k is 8.

Reason (R): Roots of the quadratic equation x² – x + 1 = 0 are real.

Find the discriminant of the quadratic equation `3x^2 - 2x + 1/3` = 0 and hence find the nature of its roots.

Find the roots of the quadratic equation x² – x – 2 = 0.

Find the value of k for which the roots of the quadratic equation 5x² – 10x + k = 0 are real and equal.

If one root of the quadratic equation 3x² – 8x – (2k + 1) = 0 is seven times the other, then find the value of k.