Factorising quadratics - (easy) Example 2

Factorise the quadratic `x^2-9x+20=0`

Quick sketch

The factors of 20 are:

1 and 20

2 and 10

4 and 5

Now ask yourself what factors of `c`  add to give `b`.

i.e. what factors of `20`  equal `-9`.

`-4times-5=20`           `-4-5=-9`

Therefore:

`x^2-9x+20=0`

Can be written as:

`(x-4)(x-5)`

Check by multiplying out:

The roots of `x^2-9x+20=0`

are `(x-4)=0`

and `(x-5)=0`

Now solve for `x`

`x=4`   or  `x=5`

Answer:

The roots of `x^2-9x+20=0`  are `x=4`  or `x=5`