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

Algebra ->  Linear-equations -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
.

Such function has the root of sqrt%287%29, which is conjugate to -sqrt%287%29
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, sqrt%287%29, -sqrt%287%29, 1+i, 1-i}.


Thus your polynomial is


    p(x) =  = 

         = x%2A%28x%5E2-7%29%2A%28%28x-1%29-i%29%2A%28%28x-1%29%2Bi%29 = x%2A%28x%5E2-7%29%2A%28%28x-1%29%5E2%2B1%29 = x%2A%28x%5E2-7%29%2A%28x%5E2+-+2x+%2B2%29.


You can transform it to any other equivalent form.

Solved.