# How do you check that you factored a quadratic correctly?

Mar 15, 2018

If both the roots satisfy the quadratic equation, then you have factorised it correctly.

#### Explanation:

I will try explaining with an example.
${x}^{2} + 4 x - 12 = 0$
The roots are $2$ and $- 6$.
Now simply put the values in the quadratic equation.

First, I will try $- 6$
${\left(- 6\right)}^{2} + 4 \left(- 6\right) - 12 = 0$
$36 - 24 - 12 = 0$
$\cancel{36} - \cancel{36} = 0$
$0 = 0$
which is true.

Now, I will try $2$
${2}^{2} + 4 \cdot 2 - 12 = 0$
$4 + 8 - 12 = 0$
$\cancel{12} - \cancel{12} = 0$
$0 = 0$
which is also true.

$\therefore$ Our answer was correct.

Hope you got it :)