Let $\lambda$ be a real number for which the system of linear equations
$$
\begin{aligned}
& x+y+z=6 \\
& 4 x+\lambda y-\lambda z=\lambda-2 \\
& 3 x+2 y-4 z=-5
\end{aligned}
$$
has infinitely many solutions. Then $\lambda$ is a root of the quadratic equation :
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