is there any way to factor x^2-x+1?

Question

Im doing the RATEY method and this was the numerator. I was trying to find the roots, but couldnt seem to figure it out. And when i put it in the calculator it showed that there was a root

Answer 1

use the quadratic formula where a=1, b=-1, and c=1

x^2-x+1

[1±√(1-4)]/2

[1±√-3]/2

[1+i√3]/2 and [1-i√3]/2, two imaginary roots