Question

find all of the zeros of p(x)= x^3+2x^2-16, given that -2-2i is a zero.(if there is more than one zero, separate them with commas.)

Answer 1

find all of the zeros of p(x)= x^3+2x^2-16, given that -2-2i is a zero.

we have that

If (2-2i) is a zero

that means

(2+2i) is a zero too by the Conjugate Zeros Theorem

using a graphing tool

the third zeros of the function is a real number

x=2

therefore

the zeros of the function are

2,(2+2i),(2-2i)