Ta có pt: \(mx^2-3\left(m+1\right)x+m^2-13m-4=0\)
Do pt có nghiệm là x = -2 nên thay vào pt ta có:
\(m\cdot\left(-2\right)^2-3\left(m+1\right)\cdot-2+m^2-13m-4=0\)
\(\Leftrightarrow4m+6\left(m+1\right)+m^2-13m-4=0\)
\(\Leftrightarrow6m+6+m^2-9m-4=0\)
\(\Leftrightarrow m^2-3m+2=0\)
\(\Delta=\left(-3\right)^2-4\cdot1\cdot2=1>0\)
\(\Leftrightarrow\left[{}\begin{matrix}m_1=\dfrac{3+\sqrt{1}}{2}=2\\m_2=\dfrac{3-\sqrt{1}}{2}=1\end{matrix}\right.\)
Nếu m = 1 thì pt là:
\(x^2-3\left(1+1\right)x+1^2-13\cdot1-4=0\)
\(\Leftrightarrow x^2-6x-16=0\)
Theo vi-et: \(x_1+x_2=-\dfrac{-6}{1}\Rightarrow x_2=6-x_2=8\)
Nếu m = 2 thì pt là:
\(2x^2-3\cdot\left(2+1\right)x+2^2-13\cdot2-4=0\)
\(\Leftrightarrow2x^2-9x-26=0\)
Theo vi-et: \(x_1+x_2=-\dfrac{-9}{2}\Leftrightarrow x_2=\dfrac{9}{2}+2=\dfrac{13}{2}\)
