Find all of the zeros of the function f(x) = x3 – 23x2 + 161x – 303.

Step-by-step explanation:

A graph shows the only real zero to be at x = 3.

Factoring that out gives the quadratic whose vertex form is ...

  y = (x -10)² +1

The roots of this quadratic are the complex numbers x = 10 ± i.

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For y = (x -10)² +1, the zeros are ...

  (x -10)² +1 = 0

  (x -10)² = -1 . . . . . . . . . . subtract 1

  x -10 = ±√(-1) = ±i . . . . .take the square root

  x = 10 ± i . . . . . . . . . . . . add 10