(English Medium) ICSE Class 10 - CISCE Question Bank Solutions for Mathematics

Solve the following quadratic equation by factorisation:
x² + 3x - 18 = 0

Solve the following quadratic equation by factorisation:
x² - 3x - 10 = 0

Solve the following quadratic equation by factorisation:
9x² - 3x - 2 = 0

Solve the following quadratic equation by factorisation:
2x² + ax - a² = 0 where a ∈ R.

Solve the following quadratic equation by factorisation method:
`x/(x + 1) + (x + 1)/x = (34)/(15') x ≠ 0, x ≠ -1`

Solve the following quadratic equation by factorisation method:
`(x + 3)/(x - 2) - (1 - x)/x = (17)/(4)`.

Solve the following quadratic equation:
4x² - 4ax + (a² - b²) = 0 where a , b ∈ R.

Solve the following by reducing them to quadratic equations:
`((7y - 1)/y)^2 - 3 ((7y - 1)/y) - 18 = 0, y ≠ 0`

Solve the following by reducing them to quadratic equations:
`sqrt(x/(1 -x)) + sqrt((1 - x)/x) = (13)/(6)`.

Solve (x² + 3x)² - (x² + 3x) -6 = 0.

Solve the following by reducing them to quadratic form:
`sqrt(y + 1) + sqrt(2y - 5) = 3, y ∈ "R".`

Solve the following by reducing them to quadratic form:
`sqrt(x^2 - 16) - (x - 4) = sqrt(x^2 - 5x + 4)`.

Solve: x(x + 1) (x + 3) (x + 4) = 180.

Solve the equation:
`6(x^2 + (1)/x^2) -25 (x - 1/x) + 12 = 0`.

Solve for x:
`(x + 1/x)^2 - (3)/(2)(x - 1/x)-4` = 0.

Solve the equation x⁴ + 2x³ - 13x² + 2x + 1 = 0.

In each of the following determine whether the given values are solutions of the equation or not.
3x² - 2x - 1 = 0; x = 1

In each of the following determine whether the given values are solutions of the equation or not.
x² + 6x + 5 = 0;  x = -1, x = -5

In each of the following determine whether the given values are solutions of the equation or not
2x² - 6x + 3 = 0; x = `(1)/(2)`

In each of the following determine whether the given values are solutions of the equation or not.
6x² - x - 2 = 0; x = `-(1)/(2), x = (2)/(3)`