a/ khi m =5
pt(1) <=> \(5x^2-5x-10=0\)
\(\Leftrightarrow x^2-x-2=0\)
Ta thấy a - b + c = 1 - (-1) - 2 = 0
=> pt có 2 nghiệm
\(\left\{{}\begin{matrix}x_1=-1\\x_2=\frac{-c}{a}=-\frac{-2}{1}=2\end{matrix}\right.\)
b/ Ta có:\(\Delta=\left(-5\right)^2-4\cdot m\cdot\left(-m-5\right)=25+4m^2+20m=\left(2m+5\right)^2\ge0\)
=> pt (1) luôn có nghiệm với mọi m
c/ Theo vi-et ta có: \(\left\{{}\begin{matrix}x_1+x_2=\frac{5}{m}\\x_1x_2=-\frac{m+5}{m}\end{matrix}\right.\)
=> \(A=-16x_1x_2-3\left(x_1^2+x_2^2\right)=-16\cdot\left(-\frac{m+5}{m}\right)-3\cdot\frac{5}{m}=\frac{16\left(m+5\right)}{m}-\frac{15}{m}=\frac{16m+80-15}{m}=\frac{16m+65}{m}\)
