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2001 Spain Mathematical Olympiad
Problem 1
Problem 1
Part of
2001 Spain Mathematical Olympiad
Problems
(1)
2001 Spanish Mathematical Olympiad, Problem 1
Source: Spanish Mathematical Olympiad 2001
6/4/2017
Prove that the graph of the polynomial
P
(
x
)
P(x)
P
(
x
)
is symmetric in respect to point
A
(
a
,
b
)
A(a,b)
A
(
a
,
b
)
if and only if there exists a polynomial
Q
(
x
)
Q(x)
Q
(
x
)
such that:
P
(
x
)
=
b
+
(
x
−
a
)
Q
(
(
x
−
a
)
2
)
)
.
P(x) = b + (x-a)Q((x-a)^2)).
P
(
x
)
=
b
+
(
x
−
a
)
Q
((
x
−
a
)
2
))
.
polynomial
geometry
algebra