Tìm m để (m+1)x^2+mx+m var DOMAIN = "https://hoc247.net/";...

* Hướng dẫn giải

\(\begin{array}{l}
\left( {m + 1} \right){x^2} + mx + m < 0,\forall x\\
 \Leftrightarrow \left\{ \begin{array}{l}
m + 1 < 0\\
\Delta  < 0
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
m <  - 1\\
 - 3{m^2} - 4m < 0
\end{array} \right.\\
 \Leftrightarrow \left\{ \begin{array}{l}
m <  - 1\\
m <  - \frac{4}{3} \vee m > 0
\end{array} \right. \Leftrightarrow m <  - \frac{4}{3}
\end{array}\)