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Possible Duplicate:
Enestrom-Kakeya Theorem

Suppose that $0, then prove that the complex polynomial $P_n(z)=a_0z^n+a_1z^{n-1}+\cdots+a_{n-1}z+a_n$ cannot have a root in the unit disc, i.e., such that $|z|<1$.

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    See also http://math.stackexchange.com/questions/188039/showing-that-the-roots-of-a-polynomial-with-descending-positive-coefficients-lie?lq=12012-09-05

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