\(\Delta=5m^2-16m+20=5\left(m-\frac{8}{5}\right)^2+\frac{36}{5}>0;\forall m\)
Phương trình luôn luôn có 2 nghiệm pb với mọi m
b/ Theo Viet: \(\left\{{}\begin{matrix}x_1+x_2=m-2\\x_1x_2=-m^2+3m-4\end{matrix}\right.\)
\(\left|\frac{x_1}{x_2}\right|=2\Leftrightarrow\left[{}\begin{matrix}x_1=2x_2\\x_1=-2x_2\end{matrix}\right.\)
- Với \(x_1=2x_2\Rightarrow\left\{{}\begin{matrix}x_1+x_2=m-2\\x_1=2x_2\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x_1=\frac{2}{3}\left(m-2\right)\\x_2=\frac{1}{3}\left(m-2\right)\end{matrix}\right.\)
\(\Rightarrow\frac{2}{9}\left(m-2\right)^2=-m^2+3m-4\)
\(\Leftrightarrow11x^2-35x+44=0\left(vn\right)\)
- Với \(x_1=-2x_2\Rightarrow\left\{{}\begin{matrix}x_1+x_2=m-2\\x_1=-2x_2\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x_1=2\left(m-2\right)\\x_2=-\left(m-2\right)\end{matrix}\right.\)
\(\Rightarrow-2\left(m-2\right)^2=-m^2+3m-4\)
\(\Leftrightarrow m^2-5m+4=0\Rightarrow\left[{}\begin{matrix}m=1\\m=4\end{matrix}\right.\)
