Question

Use the discriminant to determine the number and type of solutions for the following equation. 2x2 + 14x + 11 = 0

Answer 1

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