Author: N.K. Agakhanov
On the board, the equation $xp^3$ + * x² + * x + * = 0 is written. Peter and Vlad take turns to replace the asterisks with rational numbers: first, Peter replaces any of the asterisks, then Vlad – any of the two remaining ones, and then Peter replaces the remaining asterisk. Is it true that for any of Vlad’s actions, Peter can get an equation in which the difference of some two roots is equal to 2014?