Question

Use the discriminant to describe the roots of each equation. Then select the best description,

Answer 1

$\bf \qquad \qquad \qquad \textit{discriminant of a quadratic} \\\\\\ \stackrel{\stackrel{a}{\downarrow }}{6}x^2\stackrel{\stackrel{b}{\downarrow }}{+13}x\stackrel{\stackrel{c}{\downarrow }}{+6}=0 ~~~~~~~~ \stackrel{discriminant}{b^2-4ac}= \begin{cases} 0&\textit{one solution}\\ \underline{positive}&\textit{two solutions}\qquad \textit{\Large \checkmark}\\ negative&\textit{no solution} \end{cases} \\\\\\ 13^2-4(6)(6)\implies 169-144\implies 25$