China IMO Mock Problem: Given $xy$ is rational number, and $x$ and $y$ are the roots of the equations $6x^2+2015x+8=0$ and $6x^2+2015x+8=0$ respectively. Evaluate $\dfrac{x}{y}$.

Given $xy\ne 1$, and $x$ and $y$ are the roots of the equations $6x^2+2015x+8=0$ and $6x^2+2015x+8=0$ respectively. Evaluate $\dfrac{x}{y}$.

Solution:

Since the coefficients of $6x^2+2015x+8=0$ are the same as the coefficients of $8y^2+2015y+6$ in reversed order, and we're told that $x$ is the root of the equation $6x^2+2015x+8=0$ while $y$ is the root of the equation  $8y^2+2015y+6$.