SOLUTION: If 1 is a root of the equation x^3-5x^2+17x-13=0, find the other two roots.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: If 1 is a root of the equation x^3-5x^2+17x-13=0, find the other two roots.       Log On


   

Question 335219: If 1 is a root of the equation x^3-5x^2+17x-13=0, find the other two roots.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
If x=1 is a root then x-1 is a factor.
Use polynomial long division to find the remaining quadratic.
%28x%5E3-5x%5E2%2B17x-13%29%2F%28x-1%29
First term:x%5E2
x%5E2%28x-1%29=x%5E3-x%5E2
Subtract this product from the original polynomial to get the remainder.
%28x%5E3-5x%5E2%2B17x-13%29-%28x%5E3-x%5E2%29=-4x%5E2%2B17x-13
.
.
.
Second term:-4x%28x-1%29=-4x%5E2%2B4x
Subtract this product from the remainder to get the new remainder.
%28-4x%5E2%2B17x-13%29-%28-4x%5E2%2B4x%29=13x-13
.
.
.
Final term:13%28x-1%29=13x-13
Subtract this product from the remainder to get the final remainder.
%2813x-13%29-%2813x-13%29=0
.
.
.
Gather the terms.
%28x%5E3-5x%5E2%2B17x-13%29%2F%28x-1%29=x%5E2-4x%2B13
.
.
.
Complete the square to find the solution to the quadratic equation,
x%5E2-4x%2B13=x%5E2-4x%2B4%2B9=0
%28x-2%29%5E2%2B9=0
%28x-2%29%5E2=-9
x-2=0+%2B-+sqrt%28-9%29
x=2+%2B-+3i