# How do you find the zeros, real and imaginary, of y=x^2-x+17 using the quadratic formula?

Calculate $\Delta = {b}^{2} - 4 a c$ in order to know if which field the roots are in. The roots here are $\frac{1 \pm i \sqrt{67}}{2}$
Here, $\Delta = 1 - 4 \cdot 17 = - 67$ so this polynomial has 2 complex roots.
By the quadratic formula, the roots are given by the formula $\frac{- b \pm \sqrt{\Delta}}{2} a$.
So ${x}_{1} = \frac{1 - i \sqrt{67}}{2}$ and ${x}_{2} = \overline{{x}_{1}}$.