Let $p(x)=ax^2 + bx +c$ be a quadratic polynomial over the field $F[X]$, i.e. where the coefficients $a,b,c$ are elements of some field $(F, + , \cdot)$ and $a\neq 0$. Then the formula $p(x)=0$ has exactly two roots given by $$x_{1,2}:=\frac{-b\pm\sqrt{b^2-4ac}}{2a}.$$
Proofs: 1