2013 UMO Problems/Problem 5


Cooper and Malone take turns replacing $a$, $b$, and $c$ in the equation below with real numbers. \[P(x) = x^3 + ax^2 + bx + c.\] Once a coefficient has been replaced, no one can choose to change that coefficient on their turn. The game ends when all three coefficients have been chosen. Malone wins if $P(x)$ has a non-real root and Cooper wins otherwise. If Malone goes first, find the person who has a winning strategy and describe it with proof.


See Also

2013 UMO (ProblemsAnswer KeyResources)
Preceded by
Problem 4
Followed by
Problem 6
1 2 3 4 5 6
All UMO Problems and Solutions
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