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

Solve x^2/3 + x^1/3 - 2 = 0.

In each of the following determine the; value of k for which the given value is a solution of the equation:
kx² + 2x - 3 = 0; x = 2

In each of the following determine the; value of k for which the given value is a solution of the equation:
3x² + 2kx - 3 = 0; x = `-(1)/(2)`

In each of the following determine the; value of k for which the given value is a solution of the equation:
x² + 2ax - k = 0; x = - a.

If x = 2 and x = 3 are roots of the equation 3x² – 2kx + 2m = 0. Find the values of k and m.

Determine whether the given values of x is the solution of the given quadratic equation below:
6x² - x - 2 = 0; x = `(2)/(3), -1`.

Form the quadratic equation whose roots are:
`sqrt(3) and 3sqrt(3)`

Form the quadratic equation whose roots are:
`2 + sqrt(5) and 2 - sqrt(5)`.

Find the value of k for which the given equation has real roots:
kx² - 6x - 2 = 0

Find the value of k for which the given equation has real roots:
9x² + 3kx + 4 = 0.

Without actually determining the roots comment upon the nature of the roots of each of the following equations:
3x² + 2x - 1 = 0

Without actually determining the roots comment upon the nature of the roots of each of the following equations:
`2sqrt(3)x^2 - 2sqrt(2)x - sqrt(3) = 0`

Without actually determining the roots comment upon the nature of the roots of each of the following equations:
9a²b²x² - 48abc + 64c²d² = 0, a ≠ 0, b ≠ 0

Without actually determining the roots comment upon the nature of the roots of each of the following equations:
x² - 5x + 7 = 0

Without actually determining the roots comment upon the nature of the roots of each of the following equations:
x² - 4x + 1 = 0

Without actually determining the roots comment upon the nature of the roots of each of the following equations:
x² + 5x + 15 = 0.

Without solving the following quadratic equation, find the value of 'm' for which the given equation has real and equal roots.

x² + 2(m – 1)x + (m + 5) = 0

Solve the following by reducing them to quadratic equations:
x⁴ - 26x2 + 25 = 0

Solve the following by reducing them to quadratic equations:
z⁴ - 10z² + 9 = 0.

Solve for x : `9^(x + 2) -6.3^(x + 1) + 1 = 0`.