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 4 i are zeros; f (-1)=-170

Answer 1

Since 4i is a root, that automatically means -4i is also a root (complex roots always travel in pairs) So the factored form would look like (x+4i)(x−4i). When multiplied out this gives the polynomial x2+16.