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

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 ______.

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If the equation 2x² – 5x + (k + 3) = 0 has equal roots then the value of k is

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The value(s) of k for which the quadratic equation 2x² – kx + k = 0 has equal roots is (are)

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If the equation 3x² – kx + 2k =0 roots, then the the value(s) of k is (are)

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If the equation {k + 1)x² – 2(k – 1)x + 1 = 0 has equal roots, then the values of k are

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If the equation 2x² – 6x + p = 0 has real and different roots, then the values of p are given by

The quadratic equation `2x^2 - sqrt(5)x + 1 = 0` has ______.

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Which of the following equations has two distinct real roots?

Which of the following equations has no real roots?

Discuss the nature of the roots of the following equation: 3x² – 7x + 8 = 0

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

Discuss the nature of the roots of the following equation: `5x^2 - 6sqrt(5)x + 9` = 0

Discuss the nature of the roots of the following equation: `sqrt(3)x^2 - 2x - sqrt(3)` = 0

Find the values of k so that the quadratic equation (4 – k) x² + 2 (k + 2) x + (8k + 1) = 0 has equal roots.