Determine the number of zeros in the right half-plane (Re z > 0) of the polynomial p(2) = 23 + 22 + 9z + 4.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 29E
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8. (The argument principle and Rouché's theorem)
(a) Determine the number of zeros in the right half-plane (Re z > 0) of the polynomial
p(2) = 2* + z² + 9z + 4.
(b) Show that the equation
e= - 2:2 = 1
has exactly two solutions in the disk |z| < 1, and that they are both real.
Transcribed Image Text:8. (The argument principle and Rouché's theorem) (a) Determine the number of zeros in the right half-plane (Re z > 0) of the polynomial p(2) = 2* + z² + 9z + 4. (b) Show that the equation e= - 2:2 = 1 has exactly two solutions in the disk |z| < 1, and that they are both real.
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