$${ax^2 + bx + c = 0}$$

Solve each of the following equations.

As a general rule, each equation has got two (!) solutions.

Write down all your thoughts in your notes and comment about how the question differs from the previous one. Make sure not to expand the term in exercise no 5 and use no 5 to solve no 6.

You do not have to solve all at once. You will be given plenty of time.

Where you have square roots, make sure that

• there is no square root in the denominator, i.e. rationalise the denominator.
• you simplify each square root as far as possible.

### questions

#### no 1

$${x^2 = 4}$$

#### no 2

$${x^2 - 3 = 0}$$

#### no 3

$${2x^2 - 1 = 0}$$

#### no 4

$${x^2 = 6}$$

#### no 5

$${(x + 2)^2 = 6}$$

#### no 6

$${x^2 - 6x + 9 = \frac{25}{4}}$$

#### no 7

$${x^2 -6x = 31}$$

#### no 8

$${x^2 + 4x = - \frac{7}{4}}$$

#### no 9

$${x^2 - \frac{2}{3}x = - \frac{1}{9}}$$

#### no 10

$${x^2 - 3x = - \frac{25}{4}}$$

#### no 11

$${2x^2 + 4x - 7 = 0}$$

#### no 12

$${\frac{1}{6}x^2 - \frac{1}{4}x - \frac{1}{6} = 0}$$

#### no 13

$${x^2 + 2px + q = 0}$$

#### no 14

$${ax^2 + bx + c = 0}$$

$${x^2 + px + q = 0}$$