Concept:The nature of roots of a quadratic equation ax2+bx+c=0 is determined by the discriminant D=b2−4ac.Explanation:For the equation x2−x+1=0, we have a=1, b=−1, c=1.D=(−1)2−4(1)(1)=1−4=−3.Since D<0, the roots are imaginary (complex) and unequal (D=0).Answer:Imaginary and unequal