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2010 Irish Math Olympiad
5
Find Polynomials
Find Polynomials
Source: 2010 IrMO Paper 1 Problem 5
January 30, 2018
algebra
polynomial
Problem Statement
Find all polynomials
f
(
x
)
=
x
3
+
b
x
2
+
c
x
+
d
f(x)=x^3+bx^2+cx+d
f
(
x
)
=
x
3
+
b
x
2
+
c
x
+
d
, where
b
,
c
,
d
,
b,c,d,
b
,
c
,
d
,
are real numbers, such that
f
(
x
2
−
2
)
=
−
f
(
−
x
)
f
(
x
)
f(x^2-2)=-f(-x)f(x)
f
(
x
2
−
2
)
=
−
f
(
−
x
)
f
(
x
)
.
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