Question 38047: My teacher has our advanced algebra class taking college algebra tests just for the heck of it.
The problem asks to find a polynomial equation of degree 4 with integral coefficients that has solutions 1+i, 3, 0.
Answer by fractalier(6550)   (Show Source):
You can put this solution on YOUR website! Well one thing you have to recognize is that complex roots ALWAYS come in conjugate pairs...so that if 1 + i is a root, so is 1 - i, even if they don't give it to you...thus our polynomial must be
(x - 0)(x - 3)(x - (1 + i))(x - (1 - i)) = 0
now multiply it all out
(x^2 - 3x)(x - 1 + i)(x - 1 - i) = 0
(x^2 - 3x)(x^2 - 2x + 2) = 0
x^4 - 5x^3 + 8x^2 - 6x = 0
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