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complex roots satisfy |z|>1

Source: VJIMC 1998 2.3

August 24, 2021
algebrapolynomialcomplex numbers

Problem Statement

Show that all complex roots of the polynomial P(z)=a0zn+a1zn−1+…+an−1z+anP(z)=a_0z^n+a_1z^{n-1}+\ldots+a_{n-1}z+a_n, where 0<a0<…<an0<a_0<\ldots<a_n, satisfy ∣z∣>1|z|>1.
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