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The Modulus of a Polynomial are the Same

Source: 2018 China TST 4 Day 2 Problem 5

March 27, 2018
algebrapolynomial

Problem Statement

Suppose the real number λ∈(0,1),\lambda \in \left( 0,1\right), and let nn be a positive integer. Prove that the modulus of all the roots of the polynomial f(x)=∑k=0n(nk)λk(n−k)xkf\left ( x \right )=\sum_{k=0}^{n}\binom{n}{k}\lambda^{k\left ( n-k \right )}x^{k} are 1.1.
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