How do you find all zeros of the function f(x)=x^3(x-2)^2?

Feb 26, 2016

$x = 0 , 2$

Explanation:

To find all the zeros of the function, set each factor to $0$ and solve for $x$.

${x}^{3} = 0$
$x = \sqrt[3]{0}$
$\textcolor{g r e e n}{x = 0}$

$x - 2 = 0$
$\textcolor{g r e e n}{x = 2}$

You can see this holds true graphically as well:

graph{x^3(x-2)^2 [-5, 5, -2.5, 2.5]}

$\therefore$, the zeros of the function are $x = 0$ and $x = 2$.