\(\Leftrightarrow m\left(x^3+3x^2-4\right)+\left(x^3-x^2-x+1\right)=0\)
\(\Leftrightarrow m\left(x-1\right)\left(x^2+4x+4\right)+\left(x-1\right)\left(x^2-1\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(\left(m+1\right)x^2+4mx+4m-1\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}m=1\\\left(m+1\right)x^2+4mx+4m-1=0\left(1\right)\end{matrix}\right.\)
Pt đã cho có 3 nghiệm pb khi và chỉ khi (1) có 2 nghiệm pb khác 1
\(\Leftrightarrow\left\{{}\begin{matrix}m+1\ne0\\\Delta'=4m^2-\left(4m-1\right)\left(m+1\right)>0\\m+1+4m+4m-1\ne0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}m\ne-1\\-3m+1>0\\m\ne0\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}m\ne\left\{-1;0\right\}\\m< \dfrac{1}{3}\end{matrix}\right.\)
