Question

find a cubic polynomial equation that has the given roots of -4 and 4i

Answer 1

Hint:

if -4 is a root, then x+4 is a factor

if 4i is a root, so is -4i which means

x=+-4i

x^2 = (+-4i)^2

x^2 = 16i^2

x^2 = -16

x^2+16=0

So if 4i is a root, then x^2 + 16 is a factor