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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6210 • Real Analysis

Fall 2017 • Question 10

Question

Math 6210 • Real Analysis Fall 2017 • Question 10

Determine the number of zeroes of the polynomial \[ z^5+\frac {z^3}{3}+\frac {z^2}{4}+\frac {z}{3} \] in the region \(1/2<|z|<1\).

Raw LaTeX

Determine the number of zeroes of the polynomial
\[
z^5+\frac{z^3}{3}+\frac{z^2}{4}+\frac{z}{3}
\]
in the region \(1/2<|z|<1\).

Topic Tags

Zeros of Holomorphic Functions and the Identity Theorem