Let λ ≠ 0 be a real number. Let α, β be the roots of the equation 14 x^2-31 x+3 λ=0 and α, γ be the roots of the equation 35 x^2-53 x+4 λ=0. Then (3…

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