English Medium इयत्ता १० - CBSE Question Bank Solutions

Verify that 5, –2 and `1/3` are the zeroes of the cubic polynomial p(x) = (3x³ – 10x² – 27x + 10) and verify the relation between its zeros and coefficients.

Find a cubic polynomial whose zeroes are 2, –3 and 4.

Find a cubic polynomial whose zeroes are `1/2`, 1 and –3.

Find a cubic polynomial with the sum of its zeroes, sum of the products of its zeroes taken two at a time and the product of its zeroes as 5, –2 and –24 respectively. 

Find the quotient and the remainder when f(x) = x⁴ – 3x² + 4x + 5 is divided by g(x) = x² – x + 1.

Find the quotient and the remainder when f(x) = x⁴ – 5x + 6 is divided by g(x) = 2 – x².

By actual division, show that x² – 3 is a factor of 2x⁴ + 3x³ – 2x² – 9x – 12.

On dividing 3x³ + x² + 2x + 5 is divided by a polynomial g(x), the quotient and remainder are (3x – 5) and (9x + 10) respectively. Find g(x).

If 1 and –2 are two zeroes of the polynomial (x³ – 4x² – 7x + 10), find its third zero.

If 3 and –3 are two zeroes of the polynomial (x⁴ + x³ – 11x² – 9x + 18), find all the zeroes of the given polynomial.

If 2 and -2 are two zeroes of the polynomial `(x^4 + x^3 – 34x^2 – 4x + 120)`, find all the zeroes of the given polynomial. 

Find all the zeroes of (x⁴ + x³ – 23x² – 3x + 60), if it is given that two of its zeroes are `sqrt(3)` and `-sqrt(3)`.

If α, β are the zeroes of the polynomial f(x) = 5x² – 7x + 1 then `1/α + 1/β = ?`

If α, β are the zeroes of the polynomial f(x) = x² + x – 2, then `(α/β - α/β)`.

(i)` (1-cos^2 theta )cosec^2theta = 1`

`(1 + cot^2 theta ) sin^2 theta =1`

`(sec^2 theta-1) cot ^2 theta=1`

`(sec^2 theta -1)(cosec^2 theta - 1)=1`

`(1-cos^2theta) sec^2 theta = tan^2 theta`

`sin^2 theta + 1/((1+tan^2 theta))=1`