Question

How do you solve `x^2-x-12=0`?

Answer 1

We can Split the Middle Term of this equation and factorise it to find the solution.

In this technique, if we have to factorise an expression like `ax^2 +bx + c`, we need to think of two numbers such that:

`N_1 xx N_2 = a xx c = 1 xx (-12) = -12`

and

`N_1 +N_2 = b = -1`

After trying out a few numbers we get `N_1 = -4` and `N_2 =3`
`(-4) xx 3 = -12`, and `(-4) + 3= -1`

`x^2 -x -12 = x^2 -4x +3x -12`
`= x(x-4)+3 (x-4)`
`= (x+3)(x-4)`

the solution is `color(blue)x=-3 , color(blue)x=4`