Question:
Solve the equation $x^{2}-x+2=0$
Solution:
The given quadratic equation is $x^{2}-x+2=0$
On comparing the given equation with $a x^{2}+b x+c=0$, we obtain
$a=1, b=-1$, and $c=2$
Therefore, the discriminant of the given equation is
$D=b^{2}-4 a c=(-1)^{2}-4 \times 1 \times 2=1-8=-7$
Therefore, the required solutions are
$\frac{-b \pm \sqrt{D}}{2 a}=\frac{-(-1) \pm \sqrt{-7}}{2 \times 1}=\frac{1 \pm \sqrt{7} i}{2}$ $[\sqrt{-1}=i]$