+) \(m+2=0\Leftrightarrow m=-2\Rightarrow-2< 0\left(TM\right)\)
+) \(m+2\ne0\Leftrightarrow m\ne-2\)
\(\left(m+2\right)x^2-2\left(m+2\right)x+3m+4< 0,\forall x\in R\)
\(\Leftrightarrow\left\{{}\begin{matrix}m+2< 0\\\Delta'< 0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}m< -2\\\left(m+2\right)^2-\left(m+2\right)\left(3m+4\right)< 0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}m< -2\\-2m^2-6m-4< 0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}m< -2\\m\in\left(-\infty;-2\right)\cup\left(-1;+\infty\right)\end{matrix}\right.\)
\(\Rightarrow m\in\left(-\infty;-2\right)\)
Vậy \(m\in(-\infty;-2]\)
