Fundamental Theorem of Algebra for Quadratics Practice Test

Find all solutions in the complex numbers of $x^2-4x+5=0$. Recall: every quadratic $ax^2+bx+c=0$ has exactly 2 complex solutions counting multiplicity (2 distinct real, 1 repeated real, or 2 complex conjugates), and the discriminant $b^2-4ac$ determines the type.

For a quadratic $ax^2+bx+c=0$ with real coefficients, the discriminant $b^2-4ac$ determines whether the two complex solutions (counting multiplicity) are 2 distinct real, 1 repeated real, or 2 complex conjugates. If a quadratic has discriminant $b^2-4ac<0$, which must be true?