SOLUTION: find a polynomial function of lowest degree with rational coefficients and the following as some of its zeros. 0, -(square root)7, 1+i

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Question 1198491: find a polynomial function of lowest degree with rational coefficients and the following as some of its zeros. 0, -(square root)7, 1+i
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.

Such function has the root of , which is conjugate to 
over the field of rational numbers, and the root 1-i, conjugate to 1+i 
over the field of real numbers.


So, the full list of the roots consists of 5 numbers {0, , , 1+i, 1-i}.


Thus your polynomial is


    p(x) =  = 

         =  =  = .


You can transform it to any other equivalent form.

Solved.



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