ĐK: m>=-2/3
\(\Leftrightarrow\left|x^2-3x+2\right|=3m+2\)
\(\Leftrightarrow\left[{}\begin{matrix}x^2-3x+2=3m+2\\x^2-3x+2=-3m-2\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x^2-3x-3m=0\left(1\right)\\x^2-3x+3m+4=0\left(2\right)\end{matrix}\right.\)
Để pt có 4 nghiệm phân biệt thì (1) và (2) đều có hai nghiệm phân biệt
=>\(\left\{{}\begin{matrix}\left(-3\right)^2-4\cdot1\cdot\left(-3m\right)>0\\\left(-3\right)^2-4\cdot1\cdot\left(3m+4\right)>0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}9+12m>0\\9-4\left(3m+4\right)>0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}m>-\dfrac{3}{4}\\9-12m-16>0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}m>-\dfrac{3}{4}\\-12m-7>0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}m>-\dfrac{3}{4}\\m< -\dfrac{7}{12}\end{matrix}\right.\Leftrightarrow-\dfrac{3}{4}< m< -\dfrac{7}{12}\)
=>-2/3<=m<-7/12
