What is the degree of the simplest polynomial with integer coefficients that has 3, sqrt(3), and (3-3i) as zeros

Is it four?

yea

I'd say 5 :

( X - 3 )( X² - 3 )( X - 3 + 3i )( X - 3 - 3i )

X^5 - 9.X^4 + 33.X^3 - 27.X^2 - 108.X + 162
if I do no mistake.

This is correct, 4 would be omitting the fact complex roots come in pairs.

this, 4=non integer coefficient in your case (and mine)

This post was edited by saber_x3 on Dec 23 2014 02:47am

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