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

`(2)/x^2 - (5)/x + 2` = 0

`sqrt(3)x^2 + 11x + 6sqrt(3)` = 0

`sqrt(3)x^2 + 10x + 7sqrt(3)` = 0

ax² + (4a² - 3b)x - 12 ab = 0

Without solving the following quadratic equation, find the value of ‘p’ for which the given equation has real and equal roots:
x² + (p – 3) x + p = 0

Find the value of k for which the following equation has equal roots:
(k − 12)x² + 2(k − 12)x + 2 = 0.

If one root of the equation 2x² – px + 4 = 0 is 2, find the other root. Also find the value of p.

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