Let \(\lambda \neq 0\) be a real number. Let \(\alpha ,\beta\) be the roots of the equation \(14{\mathrm{x}}^{2}−31\math…

Let \(\lambda \neq 0\) be a real number. Let \(\alpha ,\beta\) be the roots of the equation \(14{\mathrm{x}}^{2}−31\mathrm{x}+3\lambda =0\) and \(\alpha ,\gamma\) be the roots of the equation 35x² – 53x + 4λ =0. Then \(\frac{3\alpha }{\beta }\) and \(\frac{4\alpha }{\gamma }\) are the roots of the equation

[JEE Main 2023, 29 Jan (Shift 1)]