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 4i are zeros; f(2)=-40

Answer 1

it looks like
\[f(x)=a(x-4)(x-4i)(x+4i)=a(x-4)(x^2+16)\] you can find \(a\) by setting \(f(2)=40\) and solve for \(a\)