Question

-3x^2+2x+4=y use discriminant to find the nature of the root )0,1 or 2 roots

Answer 1

`\qquad \qquad \qquad \textit{discriminant of a quadratic} \\\\\\ \stackrel{\stackrel{\textit{\small a}}{\downarrow }}{-3}x^2 \stackrel{\stackrel{\textit{\small b}}{\downarrow }}{+2}x \stackrel{\stackrel{\textit{\small c}}{\downarrow }}{+4}=y \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}}`

`(2)^2-4(-3)(4) \implies 4 - (-48) \implies 4 + 48 \implies 52 ~~ \textit{two solutions}`