Find all of the zeros of the function f (x) = x^3-17x^2+81x-65

A graph shows the function can be factored as

f (x) = (x - 1) ((x-8) ² + 1)

There is one real root and there are two complex roots. The latter can be found from the vertex form factor:

(x - 8) ² + 1 = 0

(x - 8) ² = - 1

x - 8 = ±√ (-1) = ±i

x = 8 ± i

The zeros of the function are {1, 8-i, 8+i}.