Question Find the third degree polynomial function that has an output of 320 when x = 4, and has zeros 2 and
-8i

Step-by-step explanation:

A standard polynomial in factored form is given by:

Where p and q are the zeros.

We want to find a third-degree polynomial with zeros x = 2 and x = -8i and equals 320 when x = 4.

First, by the Complex Root Theorem, if x = -8i is a root, then x = 8i must also be a root.

Therefore, we acquire:

Simplify:

Expand the second and third factors:

Hence, our function is now:

It equals 320 when x = 4. Therefore:

Solve for a. Evaluate:

So:

Our third-degree polynomial equation is:

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step-by-step explanation:

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