SOLUTION: Find the roots X^3 - X^2 + 15X - 17 = 0 If I use synthetic division, I get (X + 1)(X^2 - 2x + 17) This is where I am stuck. I need help to finish it because I can't get syn

Question 128923: Find the roots
X^3 - X^2 + 15X - 17 = 0
If I use synthetic division, I get
(X + 1)(X^2 - 2x + 17)
This is where I am stuck. I need help to finish it because I can't get synthetic division to come out right.
Thank you.
Laura
Answer by oscargut(2103) (Show Source): You can put this solution on YOUR website!
maybe you wrote wrong X^3 - X^2 + 15X - 17 = 0
i think is X^3 - X^2 + 15X +17 = 0
a simple root is x=-1 so doing the synthetic division
1 -1 15 17
-1 -1 2 -17
1 -2 17 0
and then your result is valid X^3 - X^2 + 15X +17 =(X + 1)(X^2 - 2x + 17)
then you have to solve X^2 - 2x + 17=0 but the roots of this function are not real because (-2)^2-4(1)(17)=-64<0 then the only real root is -1
and the others are (2+sqrt(-64))/2 and (2-sqrt(-64))/2
so in complex notation 1+4i and 1-4i
Then R: -1,1+4i,1-4i

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