SOLUTION: What is the degree of the simplist polynomial with integer coefficents that has sqrt(2), 2 and 2+2i as zeros?

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Question 1130240: What is the degree of the simplist polynomial with integer coefficents that has sqrt(2), 2 and 2+2i as zeros?
Found 2 solutions by Alan3354, ikleyn:
Answer by Alan3354(69443) About Me  (Show Source):
Answer by ikleyn(52799) About Me  (Show Source):
You can put this solution on YOUR website!
.
The simplest polynomial (better to say - of the lowest degree polynomial) with integer coefficients 

has partial factors


    %28x-sqrt%282%29%29%2A%28x%2Bsqrt%282%29%29 = %28x%5E2-2%29,


    (x-2),     and

    %28x-%282%2B2i%29%29%2A%28x-%282-2i%29%29 = %28%28x-2%29-2i%29%2A%28%28x-2%29%2B2i%29 = %28x-2%29%5E2+%2B+4%29.


The full polynomial is the product of these partial factors and has the degree of 2+1+2 = 5.


Completed, answered, explained and solved.


And disproved the solution by the other tutor, which is a mistake.