Question 1105788: Find a polynomial equation with integral coefficients and of lowest degree that has the following as roots
1.) -1 , 1 , and 2
2.) -2, √2 , and 1
3.) -2 , + or - i√3
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! The first is (x+1)(x-1)(x-2), the roots being the opposite sign to the factor constant.
That can be foiled out with (x^2-1)(x-2) and becomes a cubic.
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The second has roots of -2, 1, and +/- sqrt(2), since conjugate has to be part of the roots
(x+2)(x^2-2)(x-1), and that can be foiled out.
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third has factors of (x+2)(x-isqrt(3)(x+i sqrt(3))
This is (x+2)(x^2-3i^2) or (x+2)(x^2+3) and can be foiled out
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