Use the given zero to find all the zeros of the function. (Enter your answers as a comma-separated list. Include the given zero in your answer.) Function: f(x) = x^3 + x^2 + 4x + 4 Zero: 2i

Question

Use the given zero to find all the zeros of the function. (Enter your answers as a comma-separated list. Include the given zero in your answer.)

Function: f(x) = x^3 + x^2 + 4x + 4

Zero: 2i

Answer 1

Given zero: x = 2i → x - 2i = 0

This has a conjugate pair.

x = -2i → x + 2i = 0

(x + 2i)(x - 2i) = x² - 2xi + 2xi - 4i² = x² - 4(-1) = x² + 4

Do long division:

(x³ + x² + 4x + 4) ÷ (x² + 4) = x + 1

Here are the zeros: x = -1, 2i, -2i