roots of cubic game
Source: Russia 1993
October 8, 2008
conicsparabolacombinatorics unsolvedcombinatorics
Problem Statement
The expression x^3 \plus{} . . . x^2 \plus{} . . . x \plus{} ... \equal{} 0 is written on the blackboard. Two pupils alternately replace the dots by real numbers. The first pupil
attempts to obtain an equation having exactly one real root. Can his opponent spoil his efforts?