# How do you find all zeros of the function f(x) = x^2 - 12x + 20?

Apr 2, 2016

zeros of $f \left(x\right)$ are $x = 2$ and $x = 10$

#### Explanation:

$f \left(x\right) = {x}^{2} - 12 x + 20$

We look for two numbers which when multiplied together equal $20$
and which when added together equal $\left(- 12\right)$

With a bit of though we come up with $\left(- 2\right)$ and $\left(- 10\right)$
which allows us to factor:
$f \left(x\right) = {x}^{2} - 12 x + 20 = \left(x - 2\right) \left(x - 10\right)$

For $f \left(x\right)$ to be zero
either
$\textcolor{w h i t e}{\text{XXX}} \left(x - 2\right) = 0 \rightarrow x = 2$
or
$\textcolor{w h i t e}{\text{XXX}} \left(x - 10\right) = 0 \rightarrow x = 10$