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Question Id : 13264 | Context : JEE Main 2023 (30 January Evening Shift)
For $\alpha,\beta\in\mathbb{R}$, suppose the system of linear equations $\begin{aligned} x-y+z&=5,\\ 2x+2y+\alpha z&=8,\\ 3x-y+4z&=\beta \end{aligned}$ has infinitely many solutions. Then $\alpha$ and $\beta$ are the roots of:


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