Find an nth-degree polynomial function with real coefficients satisfying the given conditions.

Question

n=3

4 and 5i are zeros;

f(2)= -116

Answer 1

The complex conjugate of a complex zero must also be a zero, so the 3 zeros are

4

5i

-5i

Then

f(x) = A(x - 4)(x - 5i)(x + 5i),

with A ≠ 0.

f(x) = A(x - 4)(x² +25)

Now set

f(2) = -116

and solve for A. You can finish from here.