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Soros Olympiad in Mathematics
IV Soros Olympiad 1997 - 98 (Russia)
9.8
P(P(P(x))) = 0 if P(x) = x^2+bx+c (IV Soros Olympiad 1997-98 R3 9.8)
P(P(P(x))) = 0 if P(x) = x^2+bx+c (IV Soros Olympiad 1997-98 R3 9.8)
Source:
June 1, 2024
algebra
polynomial
Problem Statement
The equation
P
(
x
)
=
0
P(x) = 0
P
(
x
)
=
0
, where
P
(
x
)
=
x
2
+
b
x
+
c
P(x) = x^2+bx+c
P
(
x
)
=
x
2
+
b
x
+
c
, has a single root, and the equation
P
(
P
(
P
(
x
)
)
)
=
0
P(P(P(x))) = 0
P
(
P
(
P
(
x
)))
=
0
has exactly three different roots. Solve the equation
P
(
P
(
P
(
x
)
)
)
=
0.
P(P(P(x))) = 0.
P
(
P
(
P
(
x
)))
=
0.
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