Question

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

Answer 1

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}.