242

Part of 1977 All Soviet Union Mathematical Olympiad

Problems(1)

ASU 242 All Soviet Union MO 1977 game x^{10} + ?x^9 + ?x^8 + ... + ?x + 1

Source:

x^{10} + ?x^9 + ?x^8 + ... + ?x + 1

is written on the blackboard. Two players substitute (real) numbers instead of one of the question marks in turn. (

9

turns total.) The first wins if the polynomial will have no real roots. Who wins?

game strategypolynomialalgebra