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

Question

Find an nth-degree polynomial function with real coefficients satisfying the given conditions. 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)=-390

Answer 1

A polynomial with roots as given (x-5i)(x+5i)(x-4)=x^3-4x^2+25x-100.

But the value of this polynomial at -1 is -130.

In order to make f(-1) correct, the polynomial needs to be multiplied by 3...this multiplication will not change the roots.

Final answer: 3x^3-12x^2+75x-300