MathDB
Swapping coefficients gives roots

Source: 2020 CMO P6

November 27, 2019
algebrapolynomial

Problem Statement

Does there exist positive reals a0,a1,…,a19a_0, a_1,\ldots ,a_{19}, such that the polynomial P(x)=x20+a19x19+…+a1x+a0P(x)=x^{20}+a_{19}x^{19}+\ldots +a_1x+a_0 does not have any real roots, yet all polynomials formed from swapping any two coefficients ai,aja_i,a_j has at least one real root?
Back to ProblemsView on AoPS