533

Part of 1990 All Soviet Union Mathematical Olympiad

Problems(1)

ASU 533 All Soviet Union MO 1990 game with coefficients of cubic, integer roots

Source:

A game is played in three moves. The first player picks any real number, then the second player makes it the coefficient of a cubic, except that the coefficient of

x^3

is already fixed at

1

. Can the first player make his choices so that the final cubic has three distinct integer roots?

integer rootsCubicpolynomialgamegame strategyalgebra