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

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

Use factor theorem to factorise the following polynomials completely: x³ – 19x – 30

If x³ – 2x² + px + q has a factor (x + 2) and leaves a remainder 9, when divided by (x + 1), find the values of p and q. With these values of p and q, factorize the given polynomial completely.

If (x + 3) and (x – 4) are factors of x³ + ax² – bx + 24, find the values of a and b: With these values of a and b, factorise the given expression.

f 2x³ + ax² – 11x + b leaves remainder 0 and 42 when divided by (x – 2) and (x – 3) respectively, find the values of a and b. With these values of a and b, factorize the given expression.

If (2x + 1) is a factor of both the expressions 2x² – 5x + p and 2x² + 5x + q, find the value of p and q. Hence find the other factors of both the polynomials.

If 3 is a root of the quadratic equation x² – px + 3 = 0, then p is equal to ______.

In the given figure ∠BAP = ∠DCP = 70°, PC = 6 cm and CA = 4 cm, then PD : DB is ______.

Solve the following quadratic equation:

x² + 4x – 8 = 0

Give your Solution correct to one decimal place.

(Use mathematical tables if necessary.)

Factorize completely using factor theorem:

2x³ – x² – 13x – 6

The roots of the quadratic equation px² – qx + r = 0 are real and equal if ______.