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The well-known Hutchinson’s theorem states that if P be a polynomial with positive coefficients, P(x) = ∑k=0 akx k , and ak−1 ak−2ak 4 for k = 2,3, . . . ,n , then all the zeros of P are real. We obtain sufficient conditions for a real polynomial to be a sign-independently hyperbolic polynomial or to have real separated roots in the style of Hutchinson’s theorem. Mathematics subject classification (2010): 30C15, 26C10, 47B38.

On sufficient conditions for a polynomial to be sign-independently hyperbolic or to have real separated zeros