a. Em tự giải
b.
\(\Delta'=\left(m+1\right)^2-\left(m-4\right)=m^2+m+5=\left(m+\dfrac{1}{2}\right)^2+\dfrac{19}{4}>0;\forall m\)
\(\Rightarrow\) Pt luôn có 2 nghiệm pb với mọi m
c.
Theo hệ thức Viet: \(\left\{{}\begin{matrix}x_1+x_2=-2\left(m+1\right)\\x_1x_2=m-4\end{matrix}\right.\)
\(x_1^2+x_2^2+3x_1x_2=0\)
\(\Leftrightarrow\left(x_1+x_2\right)^2+x_1x_2=0\)
\(\Leftrightarrow4\left(m+1\right)^2+m-4=0\)
\(\Leftrightarrow4m^2+9m=0\Rightarrow\left[{}\begin{matrix}m=0\\m=-\dfrac{9}{4}\end{matrix}\right.\)