Factorising quadratics - (easy) Example 3

Factorise the quadratic `x^2-x-6=0`

Quick sketch

The factors of `-6`  are:

1 and 6

2 and 3

Now ask yourself what factors of c equal b.

i.e. What factors of `-6` add to give `-1`

`-3+2=-1`   and  `-3times2=-6`

Therefore:

`x^2-x-6=0`

Can be written as:

`(x-3)(x+2)=0`

Check by multiplying out

The roots of `x^2-x-6=0`

are `(x-3)=0`

and `(x+2)=0`

Now solve for `x`

`x=3`   or  `x=-2`

Answer:

The roots of `x^2-x-6=0`  are `x=3`  or `x=-2`