\(\Delta=1-4\left(m-2\right)=9-4m\ge0\Rightarrow m\le\frac{9}{4}\)
Theo định lý Viet: \(\left\{{}\begin{matrix}x_1+x_2=-1\\x_1x_2=m-2\end{matrix}\right.\)
\(x_1x_2^3+x_1^3x_2=-10\)
\(\Leftrightarrow x_1x_2\left(x_1^2+x_2^2\right)=-10\)
\(\Leftrightarrow x_1x_2\left[\left(x_1+x_2\right)^2-2x_1x_2\right]=-10\)
\(\Leftrightarrow\left(m-2\right)\left(1-2\left(m-2\right)\right)+10=0\)
\(\Leftrightarrow-2\left(m-2\right)^2+\left(m-2\right)+10=0\)
\(\Rightarrow\left[{}\begin{matrix}m-2=\frac{5}{2}\\m-2=-2\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}m=\frac{9}{2}\left(l\right)\\m=0\end{matrix}\right.\)