quadratic equations – Maths with Graham

Solve quadratic equations by factorisation

Jan 122014

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.

Jan 122014

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)