MathDB
Problems
Contests
National and Regional Contests
Russia Contests
All-Russian Olympiad
1973 All Soviet Union Mathematical Olympiad
180
180
Part of
1973 All Soviet Union Mathematical Olympiad
Problems
(1)
ASU 180 All Soviet Union MO 1973 ax^2+bx+c=x has not real roots
Source:
7/4/2019
The square polynomial
f
(
x
)
=
a
x
2
+
b
x
+
c
f(x)=ax^2+bx+c
f
(
x
)
=
a
x
2
+
b
x
+
c
is of such a sort, that the equation
f
(
x
)
=
x
f(x)=x
f
(
x
)
=
x
does not have real roots. Prove that the equation
f
(
f
(
x
)
)
=
0
f(f(x))=0
f
(
f
(
x
))
=
0
does not have real roots also.
trinomial
algebra