Question

How do you find all the zeros of `f(x) = x^3-x^2+25x-25`?

Answer 1

`x = 1, +-5 i`.

Explanation:

Sum of the coefficients = 0. So, 1 is a root.

One factor of the cubic is `(x - 1).`.

The other quadratic factor is readily seen as `(x^2+5^2)`.

`(x^2+5^2) = 0` gives the other two roots as `+- 5 i`.