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

Question 7045: find all the roots of each equation.
x^3-6x^2+6x-1=0
Answer by glabow(165) (Show Source): You can put this solution on YOUR website!
The equation 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.
so (x-1) evenly divides the original polynomial.
The quadratic can be solved using the quadratic formula, with results of

So, the roots are
, , and

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