1. $x^2+2mx+2m+3<0$
$\Delta=b^2-4ac^2=4m^2-8m-12$
Ycbt: $\Leftrightarrow \left\{ \begin{array}{l}\Delta≤0 \\a>0\end{array} \right.$
$\Leftrightarrow \left\{ \begin{array}{l}4m^2-8m-12≤0 \\1>0(ld)\end{array} \right.$
$\Leftrightarrow \left\{ \begin{array}{l}-1≤m ≤3\\1>0(ld)\end{array} \right.$
$\Leftrightarrow -1≤m≤3$ thoả ycbt
2. $x^2+m<4x$
$\Leftrightarrow x^2-4x+m<0$
$\Delta=b^2-4ac=16-4m$
Ycbt: $\Leftrightarrow \left\{ \begin{array}{l}\Delta≤0 \\a>0\end{array} \right.$
$\Leftrightarrow \left\{ \begin{array}{l}16-4m≤0 \\1>0(ld)\end{array} \right.$
$\Leftrightarrow \left\{ \begin{array}{l}m≥4 \\1>0(ld)\end{array} \right.$
$\Leftrightarrow m≥4$ thoả ycbt
