English Medium कक्षा १० - CBSE Question Bank Solutions for Mathematics

For the following, find a quadratic polynomial whose sum and product respectively of the zeroes are as given. Also find the zeroes of these polynomials by factorisation.

`21/8, 5/16`

For the following, find a quadratic polynomial whose sum and product respectively of the zeroes are as given. Also find the zeroes of these polynomials by factorisation.

`-2sqrt(3), -9`

For the following, find a quadratic polynomial whose sum and product respectively of the zeroes are as given. Also find the zeroes of these polynomials by factorisation.

`(-3)/(2sqrt(5)), -1/2`

Given that the zeroes of the cubic polynomial x³ – 6x² + 3x + 10 are of the form a, a + b, a + 2b for some real numbers a and b, find the values of a and b as well as the zeroes of the given polynomial.

Given that `sqrt(2)` is a zero of the cubic polynomial `6x^3 + sqrt(2)x^2 - 10x - 4sqrt(2)`, find its other two zeroes.

Which of the following equations has the sum of its roots as 3?

Values of k for which the quadratic equation 2x² – kx + k = 0 has equal roots is ______.

Which constant must be added and subtracted to solve the quadratic equation `9x^2 + 3/4x - sqrt(2) = 0` by the method of completing the square?

Which of the following equations has two distinct real roots?

(x² + 1)² – x² = 0 has ______.

State whether the following quadratic equation have two distinct real roots. Justify your answer.

x² – 3x + 4 = 0

State whether the following quadratic equation have two distinct real roots. Justify your answer.

2x² + x – 1 = 0

State whether the following quadratic equation have two distinct real roots. Justify your answer.

`2x^2 - 6x + 9/2 = 0`

State whether the following quadratic equation have two distinct real roots. Justify your answer.

3x² – 4x + 1 = 0

State whether the following quadratic equation have two distinct real roots. Justify your answer.

(x + 4)² – 8x = 0

Every quadratic equation has exactly one root.

Every quadratic equation has at least one real root.

A quadratic equation with integral coefficient has integral roots. Justify your answer.

Does there exist a quadratic equation whose coefficients are rational but both of its roots are irrational? Justify your answer.

Does there exist a quadratic equation whose coefficients are all distinct irrationals but both the roots are rationals? Why?