Question

Find an nth-degree polynomial function with real coefficients satisfying the given conditions. n=3. 4 and 4i are zeros, f(2) =-40

Answer 1

if \(4i\) is a zero then so is its conjugate \(-4i\) and the quadratic is
\[(x-4i)(x+4i)=x^2+16\]

Answer 2

the other zero is \(4\) to it factors as
\[a(x-4)(x^2+16)\]

Answer 3

if you want to find \(a\) put
\[f(2)=a(2-4)(2^2+16)=-40\] and solve for \(a\)