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

Question

If you are using a graphing utility, use it to graph the function and verify the real zeros and the given function value

n=3

4 and 5i are zeros

f(-1)=-260

Answer 1

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

4

5i

-5i

f(x) = A(x - 4)(x - 5i)(x + 5i) = A(x - 4)(x² + 25)

-260 = A(-1 - 4)[(-1)² + 25]

-260 = -5A(26)

A = 2

f(x) = 2(x - 4)(x² + 25)