Question

Tìm các giá trị của m để mỗi biểu thức sau luôn âm :

a) \(\left(m-4\right)x^2+\left(m+1\right)x+2m-1\)

b) \(\left(m+2\right)x^2+5x-4\)

Answer 1

a/ \(\left\{{}\begin{matrix}m-4< 0\\\Delta=\left(m+1\right)^2-4\left(m-4\right)\left(2m-1\right)< 0\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}m< 4\\-7m^2+38m-15< 0\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}m< 4\\\left[{}\begin{matrix}m< \frac{3}{7}\\m>5\end{matrix}\right.\end{matrix}\right.\)

\(\Rightarrow m< \frac{3}{7}\)

b/ \(\left\{{}\begin{matrix}m+2< 0\\\Delta=25+16\left(m+2\right)< 0\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}m< -2\\m< -\frac{57}{16}\end{matrix}\right.\) \(\Rightarrow m< -\frac{57}{16}\)