English Medium कक्षा १० - CBSE Question Bank Solutions for Mathematics

If one of the zeroes of a quadratic polynomial of the form x² + ax + b is the negative of the other, then it ______.

The only value of k for which the quadratic polynomial kx² + x + k has equal zeros is `1/2`

Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:

`v^2 + 4sqrt(3)v - 15`

Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:

`y^2 + 3/2 sqrt(5)y - 5`

Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:

`7y^2 - 11/3 y - 2/3`

The angles of a triangle are x, y and 40°. The difference between the two angles x and y is 30°. Find x and y.

The age of the father is twice the sum of the ages of his two children. After 20 years, his age will be equal to the sum of the ages of his children. Find the age of the father.

The angles of a cyclic quadrilateral ABCD are ∠A = (6x + 10)°, ∠B = (5x)°, ∠C = (x + y)°, ∠D = (3y – 10)°. Find x and y, and hence the values of the four angles. 

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

`(x - sqrt(2))^2 - 2(x + 1) = 0`

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

`sqrt(2)x^2 - 3/sqrt(2)x + 1/sqrt(2) = 0`

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

x(1 – x) – 2 = 0

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

(x – 1)(x + 2) + 2 = 0

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

(x + 1)(x – 2) + x = 0

Every quadratic equation has at least two roots.

Every quadratic equations has at most two roots.

If the coefficient of x² and the constant term of a quadratic equation have opposite signs, then the quadratic equation has real roots.

If the coefficient of x² and the constant term have the same sign and if the coefficient of x term is zero, then the quadratic equation has no real roots.

If b = 0, c < 0, is it true that the roots of x² + bx + c = 0 are numerically equal and opposite in sign? Justify.

Find the roots of the quadratic equation by using the quadratic formula in the following:

`x^2 + 2sqrt(2)x - 6 = 0`

Find the roots of the quadratic equation by using the quadratic formula in the following:

`x^2 - 3sqrt(5)x + 10 = 0`