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

Apr 25, 2016

$x = 1 , \pm 5 i$.

#### Explanation:

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

One factor of the cubic is $\left(x - 1\right) .$.

The other quadratic factor is readily seen as $\left({x}^{2} + {5}^{2}\right)$.

$\left({x}^{2} + {5}^{2}\right) = 0$ gives the other two roots as $\pm 5 i$.