\(\Delta'=\left(m+3\right)^2-\left(4m+12\right)=m^2+2m-3>0\Rightarrow\left[{}\begin{matrix}m>1\\m< -3\end{matrix}\right.\)
Theo hệ thức Viet: \(\left\{{}\begin{matrix}x_1+x_2=-2\left(m+3\right)\\x_1x_2=4m+12\end{matrix}\right.\)
Pt có 2 nghiệm lớn hơn -1 khi: \(-1< x_1< x_2\Leftrightarrow\left\{{}\begin{matrix}\left(x_1+1\right)\left(x_2+1\right)>0\\\dfrac{x_1+x_2}{2}>-1\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x_1x_2+x_1+x_2+1>0\\x_1+x_2>-2\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}4m+12-2\left(m+3\right)+1>0\\-2\left(m+3\right)>-2\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}m>-\dfrac{7}{2}\\m< -2\end{matrix}\right.\) \(\Rightarrow-\dfrac{7}{2}< m< -2\)
Kết hợp điều kiện ban đầu \(\Rightarrow-\dfrac{7}{2}< m< -3\)
