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16
factorize P(x) as a product of m real quadratic polynomials
factorize P(x) as a product of m real quadratic polynomials
Source:
September 22, 2010
algebra
polynomial
trigonometry
geometry
IMO Shortlist
factorization
Problem Statement
Given
a
,
θ
∈
R
,
m
∈
N
a, \theta \in \mathbb R, m \in \mathbb N
a
,
θ
∈
R
,
m
∈
N
, and
P
(
x
)
=
x
2
m
−
2
∣
a
∣
m
x
m
cos
θ
+
a
2
m
P(x) = x^{2m}- 2|a|^mx^m \cos \theta +a^{2m}
P
(
x
)
=
x
2
m
−
2∣
a
∣
m
x
m
cos
θ
+
a
2
m
, factorize
P
(
x
)
P(x)
P
(
x
)
as a product of
m
m
m
real quadratic polynomials.
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