Question

Answer 1

TH1: \(\Delta'=1-\left(-m+3\right)\le0\Rightarrow m\le2\)

TH2: \(\left\{{}\begin{matrix}\Delta'=m-2>0\\x_1< x_2\le2\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}m>2\\\left(x_1-2\right)\left(x_2-2\right)\ge0\\\dfrac{x_1+x_2}{2}< 2\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}m>2\\x_1x_2-2\left(x_1+x_2\right)+4\ge0\\x_1+x_2< 4\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}m>2\\-m+3-4+4\ge0\\2< 4\end{matrix}\right.\) \(\Rightarrow2< m\le3\)

Vậy \(m\le3\)