Zeros on the complex plane

zetafunction
given a finite polynomial

$$a_{0}+a_{1}x+a_{2}x^{2}+a_{3}x^{3}+............+a_{n}x^{n} =P(x)$$

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

hamster143
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?

Staff Emeritus