English Medium Class 10 - CBSE Question Bank Solutions for Mathematics

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)`.

Which term of AP 72, 68, 64, 60, ... is 0?

Which term of the AP `5/6, 1, 1 1/6, 1 1/3,` ... is 3?

Which term of the AP 21, 18, 15, ... is –81?

Which term of the AP 3,8, 13,18,…. Will be 55 more than its 20^th term?

If the 10th term of an AP is 52 and 17th term is 20 more than its 13th  term, find the AP.

Find the middle term of the AP 6, 13, 20, ..., 216.

Find the middle term of the AP 10, 7, 4, ..., (–62).

Find the sum of two middle most terms of the AP `-4/3, -1 (-2)/3, ..., 4 1/3.`