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

The roots of quadratic equation x² – 1 = 0 are ______.

While factorizing a given polynomial using the remainder and factor theorem, a student finds that (2x + 1) is a factor of 2x³ + 7x² + 2x – 3.

1. Is the student’s solution correct in stating that (2x + 1) is a factor of the given polynomial?
2. Give a valid reason for your answer.

Also, factorize the given polynomial completely.

In the given figure, AC is the diameter of the circle with center O.

CD is parallel to BE.

∠AOB = 80° and ∠ACE = 20°

Calculate:

1. ∠BEC
2. ∠BCD
3. ∠CED

The roots of equation (q – r)x² + (r – p)x + (p – q) = 0 are equal.

Prove that 2q = p + r; i.e., p, q, and r are in A.P.

If 4 is a root of equation x² + kx – 4 = 0; the value of k is ______.

The roots of the quadratic equation x² – 6x – 7 = 0 are ______.

The roots of quadratic equation x(x + 8) + 12 = 0 are ______.

If one root of equation (p – 3) x² + x + p = 0 is 2, the value of p is ______.

Equation 2x² – 3x + 1 = 0 has ______.

Which of the following equations has two real and distinct roots?

If the roots of x² – px + 4 = 0 are equal, the value (values) of p is ______.

Which of the following equations has imaginary roots?

One root of equation 3x² – mx + 4 = 0 is 1, the value of m is ______.

If the quadratic equation kx² + kx + 1 = 0 has real and distinct roots, the value of k is ______.

One factor of x³ – kx² + 11x – 6 is x – 1. The value of k is ______.

If (x – a) is a factor of x³ – ax² + x + 5; the value of a is ______.

(x – 2) is a factor of ______.

For the polynomial x⁵ – x⁴ + x³ – 8x² + 6x + 15, the maximum number of linear factors is ______.

If f(x) = 3x + 8; the value of f(x) + f(– x) is ______.

If b is the mean proportion between a and c, show that: `(a^4 + a^2b^2 + b^4)/(b^4 + b^2c^2 + c^4) = a^2/c^2`.