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Minimize a special polynomial

Source: Kürschák 1993, problem 3

July 20, 2014
algebrapolynomialalgebra unsolved

Problem Statement

Let nn be a fixed positive integer. Compute over R\mathbb{R} the minimum of the following polynomial:
f(x)=∑t=02n(2n+1−t)xt.f(x)=\sum_{t=0}^{2n}(2n+1-t)x^t.
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