SOLUTION: Find a polynomial of the lowest degree with only real coefiecients and having the given zeroes -5i amd rad 2

Question 40925: Find a polynomial of the lowest degree with only real coefiecients and having the given zeroes
-5i amd rad 2
Answer by fractalier(6550) (Show Source): You can put this solution on YOUR website!
Well, since both complex roots and irrational roots come in conjugate pairs, we know that there are a minimum of four roots here...they are � 5i and � rad(2)...thus we have
(x - 5i)(x + 5i)(x - sqrt(2))(x + sqrt(2)) = 0
now multiply it out...I'll do it in pairs...
(x^2 + 25)(x^2 - 2) = 0
x^4 + 23x^2 - 50 = 0
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