Respuesta :
[tex]\bf 8n^2-4n+2=5n\implies 8n^2-4n-5n+2=0\implies 8n^2-9n+2=0 \\\\[-0.35em] ~\dotfill\\\\ \qquad \qquad \qquad \textit{discriminant of a quadratic} \\\\\\ \stackrel{\stackrel{a}{\downarrow }}{8}n^2\stackrel{\stackrel{b}{\downarrow }}{-9}n\stackrel{\stackrel{c}{\downarrow }}{+2}=0 ~~~~~~~~ \stackrel{discriminant}{b^2-4ac}= \begin{cases} 0&\textit{one solution}\\ positive&\textit{\underline{two solutions}}\\ negative&\textit{no solution} \end{cases} \\\\\\ (-9)^2-4(8)(2)\implies 81-64\implies 17[/tex]
Answer:
2 real distinct roots.
Step-by-step explanation:
8n^2 - 4n + 2 = 5n
Rearranging to standard form:
8n^2 - 9n + 2 = 0
The discriminant = b^2 - 4ac
= (-9)^2 - 4 * 8 * 2
= 17.
So there will be 2 real distinct roots.
