For $n>1$ consider real numbers $c_0>c_1>.....>c_n>0$. Prove that the polynomial $$p(z) = c_0+c_1z+.....+c_nz^n$$ in $\mathbb{C}$ has no zero whose modulus does not exceed $1$.
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2"...has no zero whose modulus does not exceed $1$." My brain hurts. – Pedro Aug 23 '13 at 00:15
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1@AWertheim This? – Pedro Aug 23 '13 at 00:17
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1This is a well known problem. See this. Apply the transformation $q(z) = p(\frac{1}{z} ) $. – Calvin Lin Aug 23 '13 at 00:17
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That's just it, @PeterTamaroff! Thanks. :) – Alex Wertheim Aug 23 '13 at 00:23