Question

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

Answer 1

`x=0,2`

Explanation:

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

In your case:

`x^3=0`
`x=root(3)(0)`
`color(green)(x=0)`

`x-2=0`
`color(green)(x=2)`

You can see this holds true graphically as well:

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

`:.`, the zeros of the function are `x=0` and `x=2`.