Question 335219
If {{{x=1}}} is a root then {{{x-1}}} is a factor.
Use polynomial long division to find the remaining quadratic.
{{{(x^3-5x^2+17x-13)/(x-1)}}}
First term:{{{x^2}}}
{{{x^2(x-1)=x^3-x^2}}}
Subtract this product from the original polynomial to get the remainder.
{{{(x^3-5x^2+17x-13)-(x^3-x^2)=-4x^2+17x-13}}}
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Second term:{{{-4x(x-1)=-4x^2+4x}}}
Subtract this product from the remainder to get the new remainder.
{{{(-4x^2+17x-13)-(-4x^2+4x)=13x-13}}}
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Final term:{{{13(x-1)=13x-13}}}
Subtract this product from the remainder to get the final remainder.
{{{(13x-13)-(13x-13)=0}}}
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Gather the terms.
{{{(x^3-5x^2+17x-13)/(x-1)=x^2-4x+13}}}
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Complete the square to find the solution to the quadratic equation,
{{{x^2-4x+13=x^2-4x+4+9=0}}}
{{{(x-2)^2+9=0}}}
{{{(x-2)^2=-9}}}
{{{x-2=0 +- sqrt(-9)}}}
{{{x=2 +- 3i}}}