Posted by Anon on Friday, May 24, 2013 at 5:49am.
Create a 3rd degree polynomial with real coefficients that has roots 1 and 4i. Write your answer in form ax^3 + bx^2 + cx+ .

Math  Reiny, Friday, May 24, 2013 at 8:05am
any complex roots come in conjugate pairs
so if 4i is a root, so is 4i
those two roots would come from (x^2 + 16 ) = 0
so the polynomial would be
a(x+1)(x^2 + 16)
= a(x^3 + x^2 + 16x + 16)
if we assume a = 1
a possible polynomial would be
x^3 + x^2 + 16x + 16
(or any multiple of that)