Question

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

Answer 1

`\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}`