Find an​ 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; 3 and 5 i are zeros; f(2)=-29

Answer 1

To ensure real coefficients, the complex conjugate of any complex zero must also be a zero..Therefore the 3 zeros are

3

5i

-5i

The form of the polynomial is

f(x) = A(x - 3)(x - 5i)(x + 5i) = A(x - 3)(x² + 25)

with A real and A ≠ 0. Find A from setting f(2) = -29:

-29 = A(2 - 3)(2² + 25)

You can finish from here.