Question 128923
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