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All-Russian Olympiad Regional Round
2001 All-Russian Olympiad Regional Round
11.2
11.2
Part of
2001 All-Russian Olympiad Regional Round
Problems
(1)
3 roots for f(f(x)) = 0, 7 f(f(x)) = 0 - All-Russian MO 2001 Regional (R4) 11.2
Source:
9/26/2024
The monic quadratic trinomial
f
(
x
)
f(x)
f
(
x
)
has
2
2
2
different roots. Could it be that the equation
f
(
f
(
x
)
)
=
0
f(f(x)) = 0
f
(
f
(
x
))
=
0
has
3
3
3
different root, and the equation
f
(
f
(
f
(
x
)
)
)
=
0
f(f(f(x))) = 0
f
(
f
(
f
(
x
)))
=
0
has
7
7
7
different roots?
algebra
trinomial