Đáp án:
$\begin{array}{l}
b){x^2} - 2mx + 3m - 2 < 0\forall x\\
\Rightarrow \left\{ \begin{array}{l}
a < 0\\
\Delta ' < 0
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
1 < 0\left( {ktm} \right)\\
\Delta ' < 0
\end{array} \right.
\end{array}$
Vậy ko có giá trị của m thỏa mãn
$\begin{array}{l}
c){x^2} + 2\left( {m - 1} \right).x + m + 5 \ge 0\forall x\\
\Rightarrow \left\{ \begin{array}{l}
a > 0\\
\Delta ' \le 0
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
1 > 0\\
{\left( {m - 1} \right)^2} - m - 5 \le 0
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
1 > 0\\
{m^2} - 2m + 1 - m - 5 \le 0
\end{array} \right.\\
\Rightarrow {m^2} - 3m - 4 \le 0\\
\Rightarrow \left( {m - 4} \right)\left( {m + 1} \right) \le 0\\
\Rightarrow - 1 \le m \le 4\\
Vậy\, - 1 \le m \le 4\\
d)m{x^2} - 4\left( {m + 1} \right).x + m - 5 \le 0\\
+ Khi:m = 0\\
\Rightarrow - 4x - 5 \le 0\forall x\left( {ktm} \right)\\
+ Khi:m \ne 0\\
\Rightarrow \left\{ \begin{array}{l}
m < 0\\
\Delta ' \le 0
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
m < 0\\
4{\left( {m + 1} \right)^2} - m\left( {m - 5} \right) \le 0
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
m < 0\\
4{m^2} + 8m + 4 - {m^2} + 5m \le 0
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
m < 0\\
3{m^2} + 13m + 4 \le 0
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
m < 0\\
\left( {3m + 1} \right)\left( {m + 4} \right) \le 0
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
m < 0\\
- 4 \le m \le - \frac{1}{3}
\end{array} \right.\\
\Rightarrow - 4 \le m < 0\\
Vậy\, - 4 \le m < 0
\end{array}$
