Đáp án:
C10:
\( - 1 < m < \dfrac{{11}}{4}\)
Giải thích các bước giải:
\(\begin{array}{l}
C9:\\
DK:2\left( {2{m^2} - 3m - 5} \right) < 0\\
\to 2{m^2} - 3m - 5 < 0\\
\to \left( {2m - 5} \right)\left( {m + 1} \right) < 0\\
\to \left[ \begin{array}{l}
m > \dfrac{5}{2}\\
m < - 1
\end{array} \right.\\
C10:\\
f\left( x \right) > 0\forall x\\
\to 3{x^2} + 2\left( {2m - 1} \right)x + m + 4 > 0\forall x\\
\to \left\{ \begin{array}{l}
3 > 0\left( {ld} \right)\\
4{m^2} - 4m + 1 - 3\left( {m + 4} \right) < 0
\end{array} \right.\\
\to 4{m^2} - 4m + 1 - 3m - 12 < 0\\
\to 4{m^2} - 7m - 11 < 0\\
\to \left( {4m - 11} \right)\left( {m + 1} \right) < 0\\
\to - 1 < m < \dfrac{{11}}{4}
\end{array}\)
