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5
Polynomial
Polynomial
Source:
September 9, 2020
polynomial
algebra
Problem Statement
Let
P
(
x
)
∈
Z
[
x
]
P(x)\in\mathbb{Z}[x]
P
(
x
)
∈
Z
[
x
]
with deg
P
=
2015
P=2015
P
=
2015
. Let
Q
(
x
)
=
(
P
(
x
)
)
2
−
9
Q(x)=(P(x))^2-9
Q
(
x
)
=
(
P
(
x
)
)
2
−
9
. Prove that: the number of distinct roots of
Q
(
x
)
Q(x)
Q
(
x
)
can not bigger than
2015
2015
2015
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