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For polynomials f (x),g1(x),g2(x)over ℤ, we report several observations about the density of primes p for which f (x) is fully splitting at p and \left\{ {{{{g_1}\left( r \right)} \over p}} \right\} < \left\{ {{{{g_2}\left( r \right)} \over p}} \right\} for some root r of f (x) ≡ 0 mod p.