- #1

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[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] ??

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- Thread starter zetafunction
- Start date

- #1

- 391

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[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

- 907

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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

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I think he's asking what conditions make it so there are no roots with real part negative

- #4

- 907

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Ah! That makes sense.

- #5

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