Question

How do you find all the zeros of `f(x)=x^4 - x^3 - 20x^2`?

Answer 1

Factor `f(x) = x^2(x-5)(x+4)`, hence find zeros:

`x=0` (twice), `x=5` and `x=-4`

Explanation:

Separate out the common factor `x^2` of the terms, then factor the remaining quadratic using `5 xx 4 = 20` and `5 - 4 = 1` as follows:

`f(x) = x^4-x^3-20x^2`

`=x^2(x^2-x-20)`

`=x^2(x-5)(x+4)`

Hence zeros: `x=0` (twice), `x=5` and `x=-4`