RU-ALLRUSSIAN 1969 Problem 11

Given the equation $\mathrm{x}^{3} + \mathrm{ax}^{2} + \mathrm{bx} + \mathrm{c} = 0$ , the first player gives one of a, b, c an integral value. Then the second player gives one of the remaining coefficients an integral value, and finally the first player gives the remaining coefficient an integral value. The first player's objective is to ensure that the equation has three integral roots (not necessarily distinct). The second player's objective is to prevent this. Who wins?