In the last exercise you learnt how to factorise quadratic expressions. We will now use this in order to solve simple quadratic equations.

Suppose x²+9x +20 = 0

If we factorise we get (x+4) (x+5) = 0

In other words, two numbers multiply together to make 0. This means one of those numbers must be 0!

So we know EITHER x+4 = 0 OR x+5 = 0

If x +4 = 0 x = -4

If x+5 =0 then x=-5

So the solution is x = -4 or -5

Remember quadratic equations will nearly always have 2 solutions.

Try this- you will probably need pencil and paper to factorise the equations first.  To solve simple quadratic equations you need to be able to factorise quadratic expressions, like x²+9x +20

To do this look for a pair of numbers that add up to 9 and muliply together to make 20.

If you can’t find the right pair, write down all the pairs of factors of 20.

1 x 20

2 x 10

4 x 5

Now we can see the correct pair is 4 and 5.

So x²+9x +20=(x+4)(x+5)

Check this by multiplying out the brackets.

Lets try one involving negative numbers.

x² -x -12

The pairs of factors of -12 are

-12 x 1

-6 x 2

-4 x 3

-3 x 4

-2 x 6

-1 x 12

The pair that add up to -1 (because there is -x in the expression) are -4 and 3

So x² -x -12=(x-4)(x+3)

Now you try