[tex] \bf \qquad \qquad \qquad \textit{discriminant of a quadratic}
\\\\\\
y=\stackrel{\stackrel{a}{\downarrow }}{a}x^2\stackrel{\stackrel{b}{\downarrow }}{+b}x\stackrel{\stackrel{c}{\downarrow }}{+c}
~~~~~~~~
\stackrel{discriminant}{b^2-4ac}=
\begin{cases}
0&\textit{one solution}\\
positive&\textit{two solutions}\\
negative&\stackrel{\textit{no real roots}}{\textit{no solution}}\quad \checkmark
\end{cases} [/tex]
