Đáp án:
$\begin{array}{l}
C1)1){x^2} + 2x - 15 \ge 0\\
\Rightarrow {x^2} - 3x + 5x - 15 \ge 0\\
\Rightarrow \left( {x - 3} \right)\left( {x + 5} \right) \ge 0\\
\Rightarrow \left[ \begin{array}{l}
x \ge 3\\
x \le - 5
\end{array} \right.\\
\text{Vậy}\,x \ge 3\,\text{hoặc}\,x \le - 5\\
2)\left( { - x + 4} \right)\left( {{x^2} - 3x - 10} \right) < 0\\
\Rightarrow \left( {x - 4} \right)\left( {x - 5} \right)\left( {x + 2} \right) > 0\\
\Rightarrow \left[ \begin{array}{l}
\left\{ \begin{array}{l}
\left( {x - 4} \right)\left( {x - 5} \right) > 0\\
x + 2 > 0
\end{array} \right.\\
\left\{ \begin{array}{l}
\left( {x - 4} \right)\left( {x - 5} \right) < 0\\
x + 2 < 0
\end{array} \right.
\end{array} \right. \Rightarrow \left[ \begin{array}{l}
\left\{ \begin{array}{l}
\left[ \begin{array}{l}
x > 5\\
x < 4
\end{array} \right.\\
x > - 2
\end{array} \right.\\
\left\{ \begin{array}{l}
4 < x < 5\\
x < - 2
\end{array} \right.
\end{array} \right.\\
\Rightarrow \left[ \begin{array}{l}
x > 5\\
- 2 < x < 4
\end{array} \right.\\
\text{Vậy}\, - 2 < x < 4\,\text{hoặc}\,x > 5\\
3)\left\{ \begin{array}{l}
2x - 5 > 0\\
{x^2} - 7x + 6 < 0
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
x > \frac{5}{2}\\
\left( {x - 1} \right)\left( {x - 6} \right) < 0
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
x > \frac{5}{2}\\
1 < x < 6
\end{array} \right.\\
\Rightarrow \frac{5}{2} < x < 6\\
C2)1){x^2} + \left( {m - 2} \right).x + m + 1 = 0\\
\text{phương trình vô nghiệm}\\
\Rightarrow \Delta < 0\\
\Rightarrow {\left( {m - 2} \right)^2} - 4.\left( {m + 1} \right) < 0\\
\Rightarrow {m^2} - 4m + 4 - 4m - 4 < 0\\
\Rightarrow {m^2} - 8m < 0\\
\Rightarrow m\left( {m - 8} \right) < 0\\
\Rightarrow 0 < m < 8\\
\text{Vậy}\,0 < m < 8\\
2) - {x^2} + 2mx - 2020m + 2019 < 0\forall x\\
\Rightarrow \left\{ \begin{array}{l}
a = - 1 < 0\left( {tm} \right)\\
\Delta ' < 0
\end{array} \right.\\
\Rightarrow {m^2} - \left( { - 1} \right).\left( { - 2020m + 2019} \right) < 0\\
\Rightarrow {m^2} - 2020m + 2019 < 0\\
\Rightarrow \left( {m - 2019} \right)\left( {m - 1} \right) < 0\\
\Rightarrow 1 < m < 2019\\
\text{Vậy}\,1 < m < 2019
\end{array}$
