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Omni-MATH / Suppose that a polynomial of the form p(x)=x²⁰¹⁰±x²⁰⁰⁹±⋯±x±1 has no real roots. What is the maximum possible number of coefficients of -1 in p?

Problem

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problem

Suppose that a polynomial of the form p(x)=x2010±x2009±⋯±x±1p(x)=x^{2010} \pm x^{2009} \pm \cdots \pm x \pm 1 has no real roots. What is the maximum possible number of coefficients of -1 in pp?
Plain-text mathematical notation (without MathML)
Suppose that a polynomial of the form p(x)=x²⁰¹⁰±x²⁰⁰⁹±⋯±x±1 has no real roots. What is the maximum possible number of coefficients of -1 in p?
Original LaTeX notation
Suppose that a polynomial of the form $p(x)=x^{2010} \pm x^{2009} \pm \cdots \pm x \pm 1$ has no real roots. What is the maximum possible number of coefficients of -1 in $p$?

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Source and history

task_id
dde1ac84-fef5-521d-8474-d42a4a6fa19b
task_key
test--dde1ac84-fef5-521d-8474-d42a4a6fa19b
task_revision_id
1
config / split
/ test

Official source

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