Find an​ nth-degree polynomial function with real coefficients satisfying the given conditions. n = 3;
2 and 2 i are zeros;
f(-1) = 30

Step-by-step explanation:

We want to find a third degree polynomial with zeros x = 2 and x = 2i and f(-1) = 30.

First, note that by the Complex Root Theorem, since x = 2i is a root, x = -2i must also be a root.

Hence, we will have the three factors:

Where a is the leading coefficient.

Expand and simplify the second and third factors:

Hence:

Since f(-1) = 30:

In conclusion, third degree polynomial function is:

step-by-step explanation:

; fx