document.write( "Question 7045: find all the roots of each equation.
\n" ); document.write( "x^3-6x^2+6x-1=0 \n" ); document.write( "

Algebra.Com's Answer #3950 by glabow(165) $\"\"$ $\"About$

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.
\n" ); document.write( " $\"%28x%5E3-6x%5E2%2B6x-1%29%2F%28x-1%29=x%5E2%2Bx-5\"$ so (x-1) evenly divides the original polynomial.
\n" ); document.write( "The quadratic $\"x%5E2%2Bx-5\"$ can be solved using the quadratic formula, with results of
\n" ); document.write( " $\"-1+%2B-+sqrt%2821%29%2F2\"$ \r
\n" ); document.write( "\n" ); document.write( "So, the roots are
\n" ); document.write( " $\"1\"$ , $\"-1+%2B+sqrt%2821%29%2F2\"$ , and $\"+-1+-+sqrt%2821%29%2F2\"$
\n" ); document.write( " \n" ); document.write( "

\n" );