a)
\(m=6\)
\(\Rightarrow x^2+5x+6=0\)
\(\Leftrightarrow\left(x+2\right)\left(x+3\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x+2=0\\x+3=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-2\\x=-3\end{matrix}\right.\)
b)
\(\left|x_1-x_2\right|=3\)
\(\Leftrightarrow\left(x_1-x_2\right)^2=9\)
\(\Leftrightarrow x_1^2=2x_1x_2+x^2_2=9\)
\(\Leftrightarrow\left(x_1+x_2\right)^2-4x_1x_2=9\)
Mà \(\left\{{}\begin{matrix}x_1+x_2=-5\\x_1-x_2=m\end{matrix}\right.\)
\(\Rightarrow25-4m=9\)
\(\Leftrightarrow4m=16\)
\(\Leftrightarrow m=4\)