For \(\alpha, \beta \in R\), suppose the system of linear equations \(\begin{aligned}& x-y+z=5 \\& 2 x+2 y+\alph…

For \(\alpha, \beta \in R\), 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 \(\alpha\) and \(\beta\) are the roots of

[JEE Main 2023, 30 Jan (Shift 2)]