1.
\(\Leftrightarrow\Delta=\left(m-2\right)^2-8\left(-m+4\right)\le0\)
\(\Leftrightarrow m^2+4m-28\le0\)
\(\Rightarrow-2-4\sqrt{2}\le m\le-2+4\sqrt{2}\)
2.
\(\Delta'=\left(m+1\right)^2-3m^2-m< 0\)
\(\Leftrightarrow m^2+2m+1-3m^2-m< 0\)
\(\Leftrightarrow-2m^2-m+1< 0\)
\(\Rightarrow\left[{}\begin{matrix}m>\dfrac{1}{2}\\m< -1\end{matrix}\right.\)
3.
\(\Leftrightarrow x^2-\left(3m-2\right)x+2m^2-5m-2>0\) nghiệm đúng với mọi x
\(\Leftrightarrow\Delta=\left(3m-2\right)^2-4\left(2m^2-5m-2\right)< 0\)
\(\Leftrightarrow m^2+8m+12< 0\)
\(\Leftrightarrow-6< m< -2\)
4.\(\Leftrightarrow-x^2-4\left(m+1\right)x+m-5\le0\) nghiệm đúng với mọi x
\(\Leftrightarrow\Delta'=4\left(m+1\right)^2+m-5\le0\)
\(\Leftrightarrow4m^2+9m-1\le0\)
\(\Rightarrow\dfrac{-9-\sqrt{87}}{8}\le m\le\dfrac{-9+\sqrt{87}}{8}\)
