Đáp án:
\(m \in \left( { - \dfrac{7}{2};\dfrac{1}{2}} \right)\)
Giải thích các bước giải:
Để f(x)≤0 với mọi x∈R
\(\begin{array}{l}
\to \left\{ \begin{array}{l}
m - 1 < 0\\
4{m^2} + 4m + 1 - 4\left( {m - 1} \right)\left( { - 2} \right) \le 0
\end{array} \right.\\
\to \left\{ \begin{array}{l}
m < 1\\
4{m^2} + 4m + 1 + 8m - 8 \le 0
\end{array} \right.\\
\to \left\{ \begin{array}{l}
m < 1\\
4{m^2} + 12m - 7 \le 0
\end{array} \right.\\
\to \left\{ \begin{array}{l}
m < 1\\
\left( {2m - 1} \right)\left( {2m + 7} \right) \le 0
\end{array} \right.\\
\to \left\{ \begin{array}{l}
m < 1\\
m \in \left( { - \dfrac{7}{2};\dfrac{1}{2}} \right)
\end{array} \right.\\
KL:m \in \left( { - \dfrac{7}{2};\dfrac{1}{2}} \right)
\end{array}\)
