MathDB
game on polynomials

Source: Vietnam TST 2000

April 3, 2007
algebrapolynomialalgebra proposed

Problem Statement

Two players alternately replace the stars in the expression x2000+x1999+...+x+1*x^{2000}+*x^{1999}+...+*x+1 by real numbers. The player who makes the last move loses if the resulting polynomial has a real root tt with t<1|t| < 1, and wins otherwise. Give a winning strategy for one of the players.