Answer:
Step-by-step explanation:
We want to find a third degree polynomial with zeros <em>x </em>= 2 and <em>x</em> = 2i and f(-1) = 30.
First, note that by the Complex Root Theorem, since <em>x</em> = 2i is a root, <em>x</em> = -2i must also be a root.
Hence, we will have the three factors:
Where <em>a</em> is the leading coefficient.
Expand and simplify the second and third factors:
Hence:
Since f(-1) = 30:
In conclusion, third degree polynomial function is:
