We report on the converse flexoelectric effect in two bent-core nematic liquid crystals with opposite dielectric anisotropies. The results are based oil electro-optic investigations of inplane field-driven distortions in homeotropic samples (the Helfrich method). They are interpreted by an extension of the Helfrich theory that takes into account the higher order distortions. The bend flexocoefficient for both the compounds is of the usual order of magnitude as in calamitics, unlike in a previously investigated bent-core nematic for which giant values of the bend flexocoefficient are reported, In order to resolve this discrepancy, we propose a molecular model with nonpolar Clusters showing quadrupolar flexoelectricity. The Study also includes measurements on Surface polarization instabilities in the dielectrically positive material; the splay flexocoefficient thereby deduced is also of the conventional order.