MathDB
Precise bound on the unique positive root of a polynomial

Source: Germany 2020, Problem 3

June 22, 2020
inequalitiesinequalities proposedpolynomialrootsalgebra

Problem Statement

Show that the equation x(x+1)(x+2)(x+2020)1=0x(x+1)(x+2)\dots (x+2020)-1=0 has exactly one positive solution x0x_0, and prove that this solution x0x_0 satisfies 12020!+10<x0<12020!+6.\frac{1}{2020!+10}<x_0<\frac{1}{2020!+6}.