English Medium Class 10 - CBSE Question Bank Solutions

Given that: (1 + cos α) (1 + cos β) (1 + cos γ) = (1 − cos α) (1 − cos β) (1 − cos γ)

Show that one of the values of each member of this equality is sin α sin β sin γ

If sin θ + cos θ = x, prove that  `sin^6 theta + cos^6 theta = (4- 3(x^2 - 1)^2)/4`

If x = a sec θ cos ϕ, y = b sec θ sin ϕ and z = c tan θ, show that `x^2/a^2 + y^2/b^2 - z^2/c^2 = 1`

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. 

Verify that 3, –2, 1 are the zeros of the cubic polynomial p(x) = (x³ – 2x² – 5x + 6) and verify the relation between it zeros and coefficients.