MathDB
Roots of complex polynomial

Source: CMO 2022 P2

December 21, 2021
algebrapolynomial

Problem Statement

Find the largest real number λ\lambda with the following property: for any positive real numbers p,q,r,sp,q,r,s there exists a complex number z=a+biz=a+bi(a,b∈R)a,b\in \mathbb{R}) such that |b|\ge \lambda |a|   \text{and}   (pz^3+2qz^2+2rz+s) \cdot (qz^3+2pz^2+2sz+r) =0.
Back to ProblemsView on AoPS