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Zeros on the complex plane

  1. Mar 30, 2010 #1
    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] ??
  2. jcsd
  3. Mar 30, 2010 #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?
  4. Mar 30, 2010 #3


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    I think he's asking what conditions make it so there are no roots with real part negative
  5. Mar 30, 2010 #4
    Ah! That makes sense.
  6. Mar 31, 2010 #5
    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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