The polarization of the f0(1270) and ?0(770) produced in the J/ψ decays into f0γ and ?0π0 are measured in e+e? collisions at 3.1 GeV. A fit to the f0 production and decay angular distributions yields the values A1/A0 = 0.6 ± 0.3 and A2/A0 = 0.3 ?1.6+0.6, where Aλ are the f0 helicity amplitudes. These results are in good agreement with the values predicted from a QCD two-gluon-exchange model. In addition an upper limit of 2.3 × 10?4 is obtained for the J/ψ → f′0(1514) γ decay branching ratio which implies Γ(J/ψ → f′γ)/Γ(J/ψ → f0γ) ? 0.12 ± 0.05.