College algebra
posted by Jenn .
Form a polynomial f(x) with real coefficents having the given degree and zeros degree 5; zeros: 5; i; 9 +i
f(x)=a

recall that complex roots come in conjugate pairs, so the complete factorization is
(x5)(x+i)(xi)(x(9+i))(x(9i))
(x5)(x^2+1)((x+9)i)((x+9)i)
(x5)(x^2+1)((x+9)^2+1)
(x5)(x^2+1)(x^2+18x+82)
x^5+13x^47x^3397x^28x410