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Hungary-Israel Binational 1999\1

Source: Recursively defined polynomials

October 30, 2008
algebrapolynomialalgebra proposed

Problem Statement

f(x) f(x) is a given polynomial whose degree at least 2. Define the following polynomial-sequence: g_1(x)\equal{}f(x), g_{n\plus{}1}(x)\equal{}f(g_n(x)), for all n∈N n \in N. Let rn r_n be the average of gn(x) g_n(x)'s roots. If r_{19}\equal{}99, find r99 r_{99}.
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