RU-ALLRUSSIAN 1977 Problem 8

Given a polynomial $\mathrm{x}_{10} + \mathrm{a}_{9}\mathrm{x}^{9} + \ldots +\mathrm{a}_{1}\mathrm{x} + 1$ . Two players alternately choose one of the coefficients $\mathrm{a}_{1}$ to $\mathrm{a}_{9}$ (which has not been chosen before) and assign a real value to it. The first player wins iff the resulting polynomial has no real roots. Who wins?