[tex]\it mx^2+x-2=0,\ \ \forall x\in \mathbb{R} \ \Rightarrow \begin{cases}m\ \textless \ 0
\\\;\\
\Delta \ \textless \ 0 \end{cases}[/tex]
[tex]\it \Delta \ \textless \ 0 \Rightarrow 1+8m\ \textless \ 0 \Rightarrow 8m \ \textless \ -1 \Rightarrow m \ \textless \ -\dfrac{1}{8} \Rightarrow m\in\ \left(-\infty,\ -\dfrac{1}{8}\right)[/tex]