English Medium Class 9 - CBSE Question Bank Solutions

Visualise 3.765 on the number line, using successive magnification.

Visualise `4.bar26`  on the number line, up to 4 decimal places.

Determine the following polynomial has (x + 1) a factor:

x³ + x² + x + 1

Use the Factor Theorem to determine whether g(x) is a factor of p(x) in the following case:

p(x) = 2x³ + x² – 2x – 1, g(x) = x + 1

Use the Factor Theorem to determine whether g(x) is a factor of p(x) in the following case:

p(x) = x³ + 3x² + 3x + 1, g(x) = x + 2

Use the Factor Theorem to determine whether g(x) is a factor of p(x) in the following case:

p(x) = x³ − 4x² + x + 6, g(x) = x − 3

Find the value of k, if x – 1 is a factor of p(x) in the following case:

p(x) = x² + x + k

Find the value of k, if x – 1 is a factor of p(x) in the following case:

p(x) = `2x^2+kx+sqrt2`

Find the value of k, if x – 1 is a factor of p(x) in the following case:

p(x) = `kx^2 - sqrt2x +1`

Find the value of k, if x – 1 is a factor of p(x) in the following case:

p(x) = kx² – 3x + k

Factorise:

12x² – 7x + 1

Factorise:

2x² + 7x + 3

Factorise:

6x² + 5x – 6

Factorise:

3x² – x – 4

Factorise:

x³ – 2x² – x + 2

Factorise:

x³ – 3x² – 9x – 5

Factorise:

x³ + 13x² + 32x + 20

Factorise:

2y³ + y² – 2y – 1

In an isosceles triangle ABC, with AB = AC, the bisectors of ∠B and ∠C intersect each other at O. Join A to O. Show that:

1. OB = OC
2. AO bisects ∠A

In ΔABC, AD is the perpendicular bisector of BC (see the given figure). Show that ΔABC is an isosceles triangle in which AB = AC.