Find poly F(X) with lowest degree with ratio coeffs and 2 given zeros

[helpmedude]

Homework Statement

Find a polynomial function of lowest degree with rational coefficients and 2 and 3-2i as some of its zeros. Multiply the factors to make sure it has rational coefficients.

The Attempt at a Solution

zeros=2, 3-2i, 3+2i

I am not sure how write out the factors?

(x-2)(x-3+2i)(x-3-2i) is this correct?

 

[tiny-tim]

Find a polynomial function of lowest degree with rational coefficients and 2 and 3-2i as some of its zeros. Multiply the factors to make sure it has rational coefficients.
…
I am not sure how write out the factors?

(x-2)(x-3+2i)(x-3-2i) is this correct?

Yes!

hmm … it said multiply the factors … but why when they're obviously rational … hmm …

are you sure the question isn't "2 and 3 - √2i"?

 

[helpmedude]

I am not to sure. nope it is for sure 2 and 3-2i. maybe its supposed to just be an encouragement to always check ones answers.