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.

 

[Architeuthis Dux]

Yes, your work appears to be correct. You have correctly identified the remaining zeros and used them to create the factors of the polynomial. Your final answer is also in the correct form for a polynomial of degree 5. Great job!