Question

find an 5th degree polynomial with zeros at 1 and 5i and f(-1)=-104

Answer 1

5i is a complex / imaginary root. You must also consider -5i (the conjugate) in forming factors of your unknown polynomial. One such factor is (x-1).

Write out factors for 5i and -5i.

that leaves you with two unknown factors. Think about how you might identify them.

Write out your poly. that is, write (x-1)(x- ? )( x + ? ) ( x -a ) (x - b).

Now let x=-1 in your poly, and set the poly equal to the given value, -104.