# How do you find the zeros of f(x) = x^3 – 9x^2 + 20x?

Apr 5, 2016

Factor then recognizing that one of the terms must be equal to zero for the zero of the function:
$\textcolor{w h i t e}{\text{XX}} x = 0 \mathmr{and} x = 4 \mathmr{and} x = 5$

#### Explanation:

${x}^{3} - 9 {x}^{2} + 20 x$
$\textcolor{w h i t e}{\text{XXX}} = x \left({x}^{2} - 9 x + 20\right)$

$\textcolor{w h i t e}{\text{XXX}} = x \left(x - 4\right) \left(x - 5\right)$

If $f \left(x\right) = {x}^{3} - 9 x + 20 x = 0$ then
$\left\{\begin{matrix}\text{either " & x = 0 & \null \\ "or" & (x-4)=0 & rarrx=4 \\ "or} & \left(x - 5\right) = 0 & \rightarrow x = 5\end{matrix}\right.$