Abstract.Sufficient conditions on the coefficients p2", Pín-i, ' ' • ,/»o are given which guarantee that no nontrivial solution of/72"_yl2",+/»2"_iV,;!"~1,-r--• ■+/»o/=Ohas two distinct zeros each of order at least n. These conditions are in the form of n inequalities which are satisfied by linear combinations of the coefficients and their derivatives.