SOLUTION: find all the roots of each equation. x^3-6x^2+6x-1=0

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Question 7045: find all the roots of each equation.
x^3-6x^2+6x-1=0

Answer by glabow(165) About Me  (Show Source):
You can put this solution on YOUR website!
The equation x%5E3-6x%5E2%2B6x-1=0 has integer coefficients, so any root must be a factor of the coefficient of the highest term (x^3) and a factor of the lowest term (-1) in the ratio -1/1. So we expect 1 to be a zero of the polynomial.
%28x%5E3-6x%5E2%2B6x-1%29%2F%28x-1%29=x%5E2%2Bx-5 so (x-1) evenly divides the original polynomial.
The quadratic x%5E2%2Bx-5 can be solved using the quadratic formula, with results of
-1+%2B-+sqrt%2821%29%2F2
So, the roots are
1, -1+%2B+sqrt%2821%29%2F2, and +-1+-+sqrt%2821%29%2F2