Journal of the Ramanujan Mathematical Society

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A Note on The Location of Critical Points of Quintic Polynomials


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1 Department of Mathematics, Mangalore University, Mangalagangotri, 574199, India
     

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Let P (z) = (z— α) Π (z -zi) be a polynomial having all its zeros in the disk |z| < 1. In this note a new proof is given to the fact that P(z) has at least one critical point in the disk |z-α/2| < 1- |α |/2.
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  • A Note on The Location of Critical Points of Quintic Polynomials

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Authors

Sampath Kumar
Department of Mathematics, Mangalore University, Mangalagangotri, 574199, India
B. G. Shenoy
Department of Mathematics, Mangalore University, Mangalagangotri, 574199, India

Abstract


Let P (z) = (z— α) Π (z -zi) be a polynomial having all its zeros in the disk |z| < 1. In this note a new proof is given to the fact that P(z) has at least one critical point in the disk |z-α/2| < 1- |α |/2.