In this paper, we obtain a result concerning the location of zeros of a polynomial p(z)= αo+a1z+···+αnzn, where αi are complex coefficients and z is a complex variable. We obtain a ring shaped region containing all the zeros of a polynomial involving binomial coefficients and t,z-Fibonacci numbers. This result generalizes some well-known inequalities.
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Let p(z) be a polynomial of degree n and for any complex number (alfa), D(alfa)p(z) = np(z)+(alfa-z)p′(z) denote the polar derivative of the polynomial p(z) with respect to. In this paper, we obtain new results concerning maximum modulus of the polar derivative of a polynomial with restricted zeros. Our result generalize certain well-known polynomial inequalities.
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