Question

How do you find all the zeros of `f(x) = {x+1/4}^2(x - 1)^5`?

Answer 1

Observe the linear factors to see that `f(x)` has zeros:

`-1/4` with multiplicity `2`

`1` with multiplicity `5`

Explanation:

Note that linear factors correspond to zeros. The product of several factors is zeros if and only if at least one of the factors is zero.

So we can observe that `f(x)` has zeros:

`-1/4` with multiplicity `2`

`1` with multiplicity `5`

Here's a graph of `5f(x)`:

graph{5(x+1/4)^2(x-1)^5 [-0.62, 1.88, -0.54, 0.71]}