a) \(\left(2m^2-3m-2\right)x^2+2\left(m-2\right)x-1\le0\left(1\right)\)
Để \(\left(1\right)\) luôn đúng \(\forall x\in R\) khi và chỉ khi
\(\Leftrightarrow\left\{{}\begin{matrix}2m^2-3m-2\le0\\\Delta'=\left(m-2\right)^2+2m^2-3m-2\le0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}-\dfrac{1}{2}\le m\le2\\3m^2-7m+2\le0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}-\dfrac{1}{2}< m< 2\\\dfrac{1}{3}\le m\le2\end{matrix}\right.\) \(\Leftrightarrow\dfrac{1}{3}\le m\le2\)
b) Để Bpt cho vô nghiệm khi và chỉ khi
\(\Leftrightarrow\left\{{}\begin{matrix}m+4< 0\\\Delta'=m^2-2m^2-2m+24< 0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}m< -4\\m^2+2m-24>0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}m< -4\\m< -6\cup m>4\end{matrix}\right.\) \(\Leftrightarrow m< -6\)
c) Để Bpt cho đúng \(\forall x\in R\) khi và chỉ khi
\(\Leftrightarrow\left\{{}\begin{matrix}m^2-1\ge0\\\Delta'=\left(1-m\right)^2-5m^2+5\le0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}m\le-1\cup m\ge1\\4m^2+2m-6\ge0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}m\le-1\cup m\ge1\\m\le-\dfrac{3}{2}\cup m\ge2\end{matrix}\right.\)
\(\Leftrightarrow m\le-\dfrac{3}{2}\cup m\ge2\)