Chapter 2 - Linear and Quadratic Functions - Section 2.5 Inequalities Involving Quadratic Functions - 2.5 Assess Your Understanding - Page 164: 40

See explanations.

Find the discriminant of the quadratic $b^2-4ac=(-1)^2-4(1)(1)=-3\lt0$, thus the quadratic opens up and has no x-intercept meaning the curve will be above the x-axis or $x^2-x+1\gt0$ which means the original inequality will have the empty set as solution.