KöMaL 2015 B4694

Find all real numbers $p_1$, $q_1$, $p_2$, $q_2$ such that $p_2$ and $q_2$ are roots of the equation $x^3+p_1x+q_1=0$, and $p_1$ and $q_1$ are roots of the equation $x^3+p_2x+q_2=0$.