Journal of the Ramanujan Mathematical Society

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On The Location of The Critical Points of Certain Quartic Polynomials


Affiliations
1 Department of Mathematics, Mangalore University, Mangalagangotri - 574 199, India
     

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Let P(z) = (z-α) (z-Z1) [z-z2)(z-z3) be a polynomial having all its zeros in the disk |z| < 1. In this note we show that P(z) has at least one critical point in the disk |z-α/2)| <, (5-2 |α|)/6.

Keywords

Zeros of Polynomials.
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  • On The Location of The Critical Points of Certain Quartic Polynomials

Abstract Views: 259  |  PDF Views: 0

Authors

Sampath Kumar
Department of Mathematics, Mangalore University, Mangalagangotri - 574 199, India
B. G. Shenoy
Department of Mathematics, Mangalore University, Mangalagangotri - 574 199, India

Abstract


Let P(z) = (z-α) (z-Z1) [z-z2)(z-z3) be a polynomial having all its zeros in the disk |z| < 1. In this note we show that P(z) has at least one critical point in the disk |z-α/2)| <, (5-2 |α|)/6.

Keywords


Zeros of Polynomials.