English Medium कक्षा १० - CBSE Question Bank Solutions

Show that the equation 2(a² + b²)x² + 2(a + b)x + 1 = 0 has no real roots, when a ≠ b.

Prove that both the roots of the equation (x – a)(x – b) + (x – b)(x – c) + (x – c)(x – a) = 0 are real but they are equal only when a = b = c.

If a, b, c are real numbers such that ac ≠ 0, then show that at least one of the equations ax² + bx + c = 0 and –ax² + bx + c = 0 has real roots.

The equation `3x^2 – 12x + (n – 5) = 0` has equal roots. Find the value of n.

Find the zeroes of the quadratic polynomial f(x) = 4x² – 4x – 3 and verify the relation between its zeroes and coefficients.

Find the zeroes of the polynomial f(x) = `2sqrt(3)x^2 - 5x + sqrt(3)` and verify the relation between its zeroes and coefficients.

Find the zeroes of the quadratic polynomial 2x² – 11x + 15 and verify the relation between the zeroes and the coefficients.

Find the zeroes of the quadratic polynomial 4x² – 4x + 1 and verify the relation between the zeroes and the coefficients.

Find the zeroes of the quadratic polynomial` (x^2 ˗ 5)` and verify the relation between the zeroes and the coefficients.

Find the zeroes of the quadratic polynomial (8x² – 4) and verify the relation between the zeroes and the coefficients.

Find the zeroes of the quadratic polynomial `(5y^2 + 10y)` and verify the relation between the zeroes and the coefficients. 

Find the zeroes of the quadratic polynomial (3x² – x – 4) and verify the relation between the zeroes and the coefficients.

Find the quadratic polynomial whose zeroes are `2/3` and `(-1)/4`. Verify the relation between the coefficients and the zeroes of the polynomial.

Find the quadratic polynomial whose zeroes are `2/3` and `-1/4` Verify the relation between the coefficients and the zeroes of the polynomial. 

Find the quadratic polynomial, sum of whose zeroes is 8 and their product is 12. Hence, find the zeroes of the polynomial. 

Find the quadratic polynomial, sum of whose zeroes is 0 and their product is -1. Hence, find the zeroes of the polynomial. 

Find the quadratic polynomial, the sum of whose zeroes is `(5/2)` and their product is 1. Hence, find the zeros of the polynomial.

Find the quadratic polynomial, sum of whose zeroes is `sqrt2` and their product is `(1/3)`. 

If `x =2/3` and x = -3 are the roots of the quadratic equation `ax^2+2ax+5x ` then find the value of a and b.

If (x+a) is a factor of the polynomial `2x^2 + 2ax + 5x + 10`, find the value of a.