\(\Delta=25-4\left(m+4\right)=9-4m>0\Rightarrow m< \dfrac{9}{4}\)
Khi đó \(\left\{{}\begin{matrix}x_1+x_2=5\\x_1x_2=m+4\end{matrix}\right.\)
a/ \(\left\{{}\begin{matrix}3x_1+4x_2=6\\x_1+x_2=5\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x_1=14\\x_2=-9\end{matrix}\right.\)
\(\Rightarrow m+4=x_1x_2=-126\Rightarrow m=-130\)
b/ \(x_1;x_2\ne0\Rightarrow m\ne-4\)
\(\dfrac{x_1}{x_2}+\dfrac{x_2}{x_1}=-3\Leftrightarrow\dfrac{x_1^2+x_2^2}{x_1x_2}=-3\Leftrightarrow\dfrac{\left(x_1+x_2\right)^2-2x_1x_2}{x_1x_2}=-3\)
\(\Leftrightarrow\dfrac{25-2\left(m+4\right)}{m+4}=-3\Leftrightarrow17-2m=-3m-12\Rightarrow m=-29\)