This question was asked and answered fairly recently here but I don't have a specific link that I can point to. – 2012-09-05
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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=1 – 2012-09-05
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[188039] Showing that the roots of a polynomial with descending positive coefficients lie in the unit disc.
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