Question

three of the zeros of a fourth - degree polynomial function f are -5, 7, and -3i. what is the other zero of f?

Explanation:

Step1: Recall Complex Conjugate Root Theorem

For polynomials with real coefficients, complex zeros occur in conjugate pairs. If $a+bi$ is a zero, then $a-bi$ is also a zero.

Step2: Identify the complex zero

Given complex zero is $-3i$, which can be written as $0-3i$.

Step3: Find its conjugate

The conjugate of $0-3i$ is $0+3i = 3i$. Since the polynomial is 4th-degree, this is the missing zero.

Answer:

$3i$