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

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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.

Find the values of m so that the quadratic equation 3x² – 5x – 2m = 0 has two distinct real roots.

Find the value(s) of k for which each of the following quadratic equation has equal roots: 3kx² = 4(kx – 1)

Find the value(s) of k for which each of the following quadratic equation has equal roots: (k + 4)x² + (k + 1)x + 1 =0 Also, find the roots for that value (s) of k in each case.

If (x – 2) is a factor of 2x³ – x² + px – 2, then
(i) find the value of p.
(ii) with this value of p, factorise the above expression completely

When 3x² – 5x + p is divided by (x – 2), the remainder is 3. Find the value of p. Also factorise the polynomial 3x² – 5x + p – 3.

Prove that (5x + 4) is a factor of 5x³ + 4x² – 5x – 4. Hence factorize the given polynomial completely.

Use factor theorem to factorise the following polynomials completely: 4x³ + 4x² – 9x – 9