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

Discuss the nature of the roots of the following quadratic equations : `x^2 - (1)/(2)x + 4` = 0

Discuss the nature of the roots of the following quadratic equations : -2x² + x + 1 = 0

Discuss the nature of the roots of the following quadratic equations : `2sqrt(3)x^2 - 5x + sqrt(3)` = 0

Find the nature of the roots of the following quadratic equations: `x^2 - (1)/(2)x - (1)/(2)` = 0

Find the nature of the roots of the following quadratic equations: `x^2 - 2sqrt(3)x - 1` = 0 If real roots exist, find them.

Without solving the following quadratic equation, find the value of ‘p’ for which the given equations have real and equal roots: px² – 4x + 3 = 0

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

Find the value (s) of k for which each of the following quadratic equation has equal roots : kx² – 4x – 5 = 0

Find the value (s) of k for which each of the following quadratic equation has equal roots : (k – 4) x² + 2(k – 4) x + 4 = 0

Find the value(s) of m for which each of the following quadratic equation has real and equal roots: (3m + 1)x² + 2(m + 1)x + m = 0

Find the values of k for which each of the following quadratic equation has equal roots: 9x² + kx + 1 = 0 Also, find the roots for those values of k in each case.

Find the values of k for which each of the following quadratic equation has equal roots: x² – 2kx + 7k – 12 = 0 Also, find the roots for those values of k in each case.

Find the value(s) of p for which the quadratic equation (2p + 1)x² – (7p + 2)x + (7p – 3) = 0 has equal roots. Also find these roots.

If – 5 is a root of the quadratic equation 2x² + px – 15 = 0 and the quadratic equation p(x² + x) + k = 0 has equal roots, find the value of k.

Find the value(s) of p for which the equation 2x² + 3x + p = 0 has real roots.

Find the least positive value of k for which the equation x² + kx + 4 = 0 has real roots.

Find the values of p for which the equation 3x² – px + 5 = 0 has real roots.

Find the value(s) of m for which each of the following quadratic equation has real and equal roots: x² + 2(m – 1) x + (m + 5) = 0

Which of the following equations has 2 as a root?

If `(1)/(2)` is a root of the equation `x^2 + kx - (5)/(4) = 0`, then the value of k is ______.