Complex Zeros of a Polynomial Function Question

[jcsolis]

Homework Statement

find a polynomial of degree 5 whose coefficients are that has the zeros: 0, -2i, 2+i

Homework Equations

none

The Attempt at a Solution

I know that the two remaining zeros are: 2i and 2-i

the factors are:

x
x-2i
x+2i
x-2-i
x-2+i

After expand all the factors I fininshed with this answer:

f(x)= x^5 - 4x^4 + 9x^3 - 16x^2 + 20x

can somebody check if my work is OK?

 

[HallsofIvy]

Why don't you check it yourself? That certainly is a "polynomial of degree 5". You can put x= 0, x= -2i, and x= 2+ i into that polynomial and see if it is equal to 0.