\(\Delta'=\left(m+3\right)^2-4m-2=\left(m+1\right)^2+6>0;\forall m\)
Pt luôn có 2 nghiệm pb thỏa mãn \(\left\{{}\begin{matrix}x_1+x_2=-2m-6\\x_1x_2=4m+2\end{matrix}\right.\)
Để 2 nghiệm của pt đều nhỏ hơn -1 \(\Leftrightarrow x_1< x_2< -1\)
\(\Leftrightarrow\left\{{}\begin{matrix}\left(x_1+1\right)\left(x_2+1\right)>0\\\frac{x_1+x_2}{2}< -1\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x_1x_2+x_1+x_2+1>0\\x_1+x_2< -2\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}-2m-6+4m+2+1>0\\-2m-6< -2\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}m>\frac{3}{2}\\m>-2\end{matrix}\right.\) \(\Rightarrow m>\frac{3}{2}\)
