MathDB

A

and

B

play the following game with a polynomial of degree at least 4: x^{2n} \plus{} \_x^{2n \minus{} 1} \plus{} \_x^{2n \minus{} 2} \plus{} \ldots \plus{} \_x \plus{} 1 \equal{} 0

A

and

B

take turns to fill in one of the blanks with a real number until all the blanks are filled up. If the resulting polynomial has no real roots,

A

wins. Otherwise,

B

wins. If

A

begins, which player has a winning strategy?

Problem Statement