English Medium कक्षा १० - CBSE Question Bank Solutions

If the sum of the zeros of the quadratic polynomial f(t) = kt² + 2t + 3k is equal to their product, find the value of k.

If one zero of the quadratic polynomial f(x) = 4x² – 8kx – 9 is negative of the other, find the value of k.

If α and β are the zeros of the quadratic polynomial f(x) = x² – 1, find a quadratic polynomial whose zeros are `(2alpha)/beta` and `(2beta)/alpha`.

If α and β are the zeros of the quadratic polynomial f(x) = x² − 3x − 2, find a quadratic polynomial whose zeroes are `1/(2alpha+beta)+1/(2beta+alpha)`

If α and β are the zeros of a quadratic polynomial such that α + β = 24 and α – β = 8, find a quadratic polynomial having α and β as its zeros.

If α and β are the zeros of the quadratic polynomial f(x) = x² – p(x + 1) – c, show that (α + 1)(β + 1) = 1 – c.

If If α and β are the zeros of the quadratic polynomial f(x) = x² – 2x + 3, find a polynomial whose roots are α + 2, β + 2.

If If α and β are the zeros of the quadratic polynomial f(x) = x² – 2x + 3, find a polynomial whose roots are `(alpha-1)/(alpha+1)` , `(beta-1)/(beta+1)`

If α and β are the zeroes of the polynomial f(x) = x² + px + q, form a polynomial whose zeroes are (α + β)² and (α − β)².

Find a cubic polynomial with the sum, sum of the product of its zeros taken two at a time, and product of its zeros as 3, –1 and –3 respectively.

If the zeros of the polynomial f(x) = 2x³ – 15x² + 37x – 30 are in A.P., find them.

Find the condition that the zeros of the polynomial f(x) = x³ + 3px² + 3qx + r may be in A.P.

If the zeros of the polynomial f(x) = ax³ + 3bx² + 3cx + d are in A.P., prove that 2b³ – 3abc + a²d = 0.

If the zeros of the polynomial f(x) = x³ – 12x² + 39x + k are in A.P., find the value of k.

Prove the following trigonometric identities:

(1 – cos² A) cosec² A = 1

Prove the following trigonometric identities:

(1 + cot² A) sin² A = 1

Prove the following trigonometric identities.

tan²θ cos²θ = 1 − cos²θ

Prove the following trigonometric identities.

`"cosec" theta sqrt(1 - cos^2 theta) = 1`

Prove the following trigonometric identities.

(sec² θ − 1) (cosec² θ − 1) = 1

Prove the following trigonometric identities.

`tan theta + 1/tan theta` = sec θ.cosec θ