For α, β ∈ R, suppose the system of linear equations x-y+z=5; 2 x+2 y+α z=8; 3 x-y+4 z=β has infinitely many solutions. Then α and β are the roots of

For $\displaystyle \alpha, \beta \in \mathbb{R}$, suppose the system of linear equations $$\begin{aligned} & x-y+z=5 \\ & 2 x+2 y+\alpha z=8 \\ & 3 x-y+4 z=\beta \end{aligned} $$ has infinitely many solutions. Then $\displaystyle \alpha$ and $\displaystyle \beta$ are the roots of