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Omni-MATH / A and B play the following game with a polynomial of degree at least 4:

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

A A and B 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 A and B 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 A wins. Otherwise, B B wins. If A A begins, which player has a winning strategy?
Plain-text mathematical notation (without MathML)
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?
Original LaTeX notation
$ 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?

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Source and history

task_id
b8cf5c93-821c-52f0-be8d-5c872acb006a
task_key
test--b8cf5c93-821c-52f0-be8d-5c872acb006a
task_revision_id
1
config / split
/ test

Official source

initial import