Complex Numbers and Quadratic Equations: JEE Main 2023 Mathematics question

Let $\lambda \ne 0$ be a real number. Let $\alpha,\beta$ be the roots of the equation $14{x^2} - 31x + 3\lambda = 0$ and $\alpha,\gamma$ be the roots of the equation $35{x^2} - 53x + 4\lambda = 0$. Then ${{3\alpha } \over \beta }$ and ${{4\alpha } \over \gamma }$ are the roots of the equation