[tex]\bf \qquad \qquad \qquad \textit{discriminant of a quadratic} \\\\\\ \stackrel{\stackrel{a}{\downarrow }}{1}x^2\stackrel{\stackrel{b}{\downarrow }}{+2}x\stackrel{\stackrel{c}{\downarrow }}{+8}=0 ~~~~~~~~ \stackrel{discriminant}{b^2-4ac}= \begin{cases} 0&\textit{one root}\\ positive&\textit{two roots}\\ negative&\textit{no real roots}~~\textit{\Large \checkmark} \end{cases} \\\\\\ (2)^2-4(1)(8)\implies 4-32\implies -28[/tex]
