Question 7
The equation $x^3+*x^2+*x+*=0$ is written on a board. Petya and Vasya take turns replacing stars by rational numbers: first Petya replaces any star, then Vasya replaces either of the two remaining stars, and finally Petya replaces the last star. Is it true that, whatever Vasya does, Petya can obtain an equation for which the difference between two roots is $2014$?