# How do you find the zeroes for #f(x)=x^3(x-2)^2#?

##### 1 Answer

Dec 9, 2015

#### Explanation:

A zero is any point where

So, we have to find when

Notice how there are terms being multiplied by one another, equaling

So, to solve this, we can split apart

We can say that any of these are true:

or

Solve for both of these:

Therefore

Look at a graph:

graph{x^3(x-2)^2 [-3.96, 7.14, -1.19, 4.357]}

The two zeros are indeed located at