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compute the value of the discriminant and give the number of real solutions of the quadratic equations

compute the value of the discriminant and give the number of real solutions of the-example-1

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\qquad \qquad \qquad \textit{discriminant of a quadratic} \\\\\\ y=\stackrel{\stackrel{a}{\downarrow }}{2}x^2\stackrel{\stackrel{b}{\downarrow }}{-7}x\stackrel{\stackrel{c}{\downarrow }}{+9} ~~~~~~~~ \stackrel{discriminant}{b^2-4ac}= \begin{cases} 0&\textit{one solution}\\ positive&\textit{two solutions}\\ negative&\textit{no solution} \end{cases} \\\\\\ (-7)^2 - 4(2)(9)\implies 49-72\implies -23\qquad \textit{no solutions}

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