Bất phương trình $mx^{2} - 2\left ( m + 1 \right )x + m - 2 > 0$ có nghiệm
$\Leftrightarrow \left\{\begin{matrix}m > 0\\ \Delta' < 0\end{matrix}\right.$
$\Leftrightarrow \left\{\begin{matrix}m > 0\\ \left ( m + 1 \right )^{2} - m\left ( m - 2 \right ) < 0\end{matrix}\right.$
$\Leftrightarrow \left\{\begin{matrix}m > 0\\ m^{2} + 2m + 1 - m^{2} + 2m < 0\end{matrix}\right.$
$\Leftrightarrow \left\{\begin{matrix}m > 0\\ 4m + 1 < 0\end{matrix}\right.$
$\Leftrightarrow \left\{\begin{matrix}m > 0\\ m < -\dfrac{1}{4}\end{matrix}\right.$
$\Leftrightarrow m \in \varnothing$
