Quadratic Equations Factorisation and Roots

Question 1

Factorise the quadratic expression x² + 5x + 6.

Accepted Answer

(x + 2)(x + 3)

Question 2

Factorise the quadratic expression x² – 9.

Accepted Answer

(x + 3)(x - 3)

Question 3

Factorise the quadratic expression x² – 7x + 12.

Accepted Answer

(x - 3)(x - 4)

Question 4

Solve by factorisation: x² + 3x – 10 = 0.

Accepted Answer

x = 2 or x = -5

Question 5

Find the roots of x² – 5x + 4 = 0 using factorisation.

Accepted Answer

x = 1 or x = 4

Question 6

Expand the product (x + 4)(x – 3).

Accepted Answer

x² + x – 12

Question 7

Expand the product (2x + 1)(x – 5).

Accepted Answer

2x² - 9x - 5

Question 8

For the equation x² – 4x + 3 = 0, what is the sum of its roots?

Accepted Answer

4

Question 9

For the same equation x² – 4x + 3 = 0, what is the product of its roots?

Accepted Answer

3

Question 10

Which of the following quadratics cannot be factorised over the integers?

Accepted Answer

x² + x + 1

Factorise the quadratic expression x² + 5x + 6.