Question

Find the discriminant and tell how many solutions exist: -2x^2 + 4x -8 =-6

Answer 1

`\hspace{34em}|\\ -2x^2+4x-8=-6\implies -2x^2+4x-2=0 \\\\[-0.35em] ~\dotfill\\\\ ~~ \hspace{5em} \textit{discriminant of a quadratic}`

`\stackrel{\stackrel{\textit{\small a}}{\downarrow }}{-2}x^2 \stackrel{\stackrel{\textit{\small b}}{\downarrow }}{+4}x \stackrel{\stackrel{\textit{\small c}}{\downarrow }}{-2}=0 \hfill \stackrel{discriminant}{b^2-4ac}~~ = ~~ \stackrel{ \textit{\large \underline{Number of Solutions}} }{\begin{cases} ~~ ~~ 0&\textit{one solution}\\ positive&\textit{two solutions}\\ negative&\textit{no solution}\\ \end{cases}} \\\\\\ (4)^2-4(-2)(-2) \implies 16 - 16 \implies 0 ~~ \textit{one solution}`