[tex] \bf \qquad \qquad \qquad \textit{discriminant of a quadratic}
\\\\\\
\stackrel{\stackrel{a}{\downarrow }}{2}x^2\stackrel{\stackrel{b}{\downarrow }}{+14}x\stackrel{\stackrel{c}{\downarrow }}{+11}
~~~~~~~~
\stackrel{discriminant}{b^2-4ac}=
\begin{cases}
0&\textit{one solution}\\
\underline{positive}&two~\stackrel{rational}{solutions}\\
negative&\textit{no solution}
\end{cases}
\\\\\\
14^2-4(2)(11)\implies 108\impliedby \underline{positive} [/tex]
