MathDB

Roots on the board

Source: St Petersburg Olympiad 2013, Grade 10, P4

October 13, 2017

algebra

Problem Statement

There are

100

numbers from

(0,1)

on the board. On every move we replace two numbers

a,b

with roots of

x^2-ax+b=0

(if it has two roots). Prove that process is not endless.