Find a polynomial of lowest degree with rational coefficients that has the given numbers as some of its zeros? -4i, 5

My teacher did a terrible job explaining and I was hoping I could get a better explanation of how to work these kinds of problems out.

1 Answer
Feb 25, 2018

Answer:

#x^3-5x^2+16x-80#

Explanation:

#5, 4i, -4i#

So

#(x-4i)(x+4i)(x-5) " " #Subtract all from #x#

#(x^2-4ix+4ix-16i^2)(x-5) " "# FOIL the first two paratheses

#(x^2-16i^2)(x-5)" "# Cancel the #4i# terms

#(x^2+16)(x-5) " "i^2 =-1#, so multiply #-16# by #-1#

#x^3-5x^2+16x-80" "# FOIL the remaining paratheses