Question

Create a 3rd degree polynomial with real coefficients that has roots -1 and 4i. Write your answer in form ax^3 + bx^2 + cx+ .

Answer 1

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)