Zeros on the complex plane

  • #1
391
0

Main Question or Discussion Point

given a finite polynomial

[tex] a_{0}+a_{1}x+a_{2}x^{2}+a_{3}x^{3}+............+a_{n}x^{n} =P(x)[/tex]

is there a theorem or similar to ensure that P(x) has NO roots on the left of complex plane defined by [tex] Re(x<0) [/tex] ??
 

Answers and Replies

  • #2
907
2
What restrictions do you put on coefficients?

If you put n = 1, a_0 = 1, a_1 = 1, you get a polynomial with a root x=-1 on the left of complex plane right away. Perhaps I did not understand your question?
 
  • #3
Office_Shredder
Staff Emeritus
Science Advisor
Gold Member
3,750
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I think he's asking what conditions make it so there are no roots with real part negative
 
  • #4
907
2
Ah! That makes sense.
 
  • #5
1,838
7
Map the left of the complex plane to the unit disk via a conformal map (you need the möbius map) and then count the zeroes by evaluating the integral of f'/f.
 

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