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MathLinks Contest 2nd
4.1
0241 functional 2nd edition Round 4 p1
0241 functional 2nd edition Round 4 p1
Source:
May 10, 2021
algebra
functional
Problem Statement
The real polynomial
f
∈
R
[
X
]
f \in R[X]
f
∈
R
[
X
]
has an odd degree and it is given that
f
f
f
is co-prime with
g
(
x
)
=
x
2
−
x
−
1
g(x) = x^2 - x - 1
g
(
x
)
=
x
2
−
x
−
1
and
f
(
x
2
−
1
)
=
f
(
x
)
f
(
−
x
)
,
∀
x
∈
R
.
f(x^2 - 1) = f(x)f(-x), \forall x \in R.
f
(
x
2
−
1
)
=
f
(
x
)
f
(
−
x
)
,
∀
x
∈
R
.
Prove that
f
f
f
has at least two complex non-real roots.
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