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2004 Irish Math Olympiad
4
Only two real roots
Only two real roots
Source: Ireland 2004
January 2, 2007
symmetry
Problem Statement
Prove that there are only two real numbers
x
x
x
such that
(
x
−
1
)
(
x
−
2
)
(
x
−
3
)
(
x
−
4
)
(
x
−
5
)
(
x
−
6
)
=
720
(x-1)(x-2)(x-3)(x-4)(x-5)(x-6) = 720
(
x
−
1
)
(
x
−
2
)
(
x
−
3
)
(
x
−
4
)
(
x
−
5
)
(
x
−
6
)
=
720
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