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National and Regional Contests
Kyrgyzstan Contests
Kyrgyzstan National Olympiad
2016 Kyrgyzstan National Olympiad
5
5
Part of
2016 Kyrgyzstan National Olympiad
Problems
(1)
polynomials
Source: KGZ national 2016 5-problem
5/10/2016
Given two monic polynomials
P
(
x
)
P(x)
P
(
x
)
and
Q
(
x
)
Q(x)
Q
(
x
)
with degrees 2016.
P
(
x
)
=
Q
(
x
)
P(x)=Q(x)
P
(
x
)
=
Q
(
x
)
has no real root. Prove that P(x)=Q(x+1) has at least one real root.
Polynomials
algebra
polynomial