English Medium इयत्ता १० - CBSE Question Bank Solutions

The zeroes of the quadratic polynomial x² + 99x + 127 are ______.

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`

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`

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

`1/2x^2 - sqrt(11)x + 1 = 0`

Find whether the following equation have real roots. If real roots exist, find them.

`1/(2x - 3) + 1/(x - 5) = 1, x ≠ 3/2, 5`