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6
2010 Algebra #6: Fill in the Signs
2010 Algebra #6: Fill in the Signs
Source:
July 15, 2012
algebra
polynomial
Problem Statement
Suppose that a polynomial of the form
p
(
x
)
=
x
2010
±
x
2009
±
⋯
±
x
±
1
p(x)=x^{2010}\pm x^{2009}\pm \cdots \pm x \pm 1
p
(
x
)
=
x
2010
±
x
2009
±
⋯
±
x
±
1
has no real roots. What is the maximum possible number of coefficients of
−
1
-1
−
1
in
p
p
p
?
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