The space Pold CPd of all complex-valued binary forms of degree d (considered up to a constant factor) has a standard stratification, each stratum of which contains all forms whose set of multiplicities of their distinct roots is given by a fixed partition μ d. For each such stratum Sμ, we introduce its secant degeneracy index μ which is the minimal number of projectively dependent pairwise distinct points on Sμ, i.e., points whose projective span has dimension smaller than μ − 1. In what follows we discuss the secant degeneracy index μ and the secant degeneracy index μ¯ of the closure S¯ μ. Keyw

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