Question

Use the discriminant to determine the number. And type of solutions for the equation 9x^2 +6x=-1

Answer 1

`9x^2+6x=-1\implies 9x^2+6x+1=0`

`\qquad \qquad \qquad \textit{discriminant of a quadratic} \\\\\\ \stackrel{\stackrel{\textit{\small a}}{\downarrow }}{9}x^2\stackrel{\stackrel{\textit{\small b}}{\downarrow }}{+6}x\stackrel{\stackrel{\textit{\small c}}{\downarrow }}{+1}=0 ~~~~~~~~ \stackrel{discriminant}{b^2-4ac}= \begin{cases} 0&\textit{one solution}\\ positive&\textit{two solutions}\\ negative&\textit{no solution} \end{cases} \\\\\\ (6)^2 - 4(9)(1)\implies 36-36\implies 0\qquad \textit{one real solution}`