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

In the following figure, AD is the diameter of the circle with centre O. chords AB, BC and CD are equal. If ∠DEF = 110°, Calculate: ∠FAB.

Determine, if 3 is a root of the given equation
`sqrt(x^2 - 4x + 3) + sqrt(x^2 - 9) = sqrt(4x^2 - 14x + 16)`.

Find if x = – 1 is a root of the equation 2x² – 3x + 1 = 0.

(3x - 5)(2x + 7) = 0

48x² – 13x -1 = 0

`10x -(1)/x` = 3

`(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)`