  We give a formula in terms of multidimensional resultants for an equation for
the flex locus of a projective hypersurface, generalizing a classical result of
Salmon for surfaces. Using this formula, we compute the dimension of this flex
locus, and an upper bound for the degree of its defining equations. We also
show that, when the hypersurface is generic, this bound is reached, and that
the generic flex line is unique and has the expected order of contact with the
hypersurface.
