Question

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

Answer 1

`f(x)` has zeros `1` and `+-2i`

Explanation:

Note that the ratio of the first and second terms is the same as that between the third and fourth. So this cubic factors by grouping:

`x^3-x^2+4x-4`

`=x^2(x-1)+4(x-1)`

`=(x^2+4)(x-1)`

`=(x^2-(2i)^2)(x-1)`

`=(x-2i)(x+2i)(x-1)`

Hence zeros: `+-2i` and `1`