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National and Regional Contests
Russia Contests
All-Russian Olympiad Regional Round
1998 All-Russian Olympiad Regional Round
10.1
10.1
Part of
1998 All-Russian Olympiad Regional Round
Problems
(1)
f(x) = x^2 + ax + b cos x - All-Russian MO 1998 Regional (R4) 10.1
Source:
9/17/2024
Let
f
(
x
)
=
x
2
+
a
x
+
b
c
o
s
x
f(x) = x^2 + ax + b cos x
f
(
x
)
=
x
2
+
a
x
+
b
cos
x
. Find all values of parameter
a
a
a
and
b
b
b
, for which the equations
f
(
x
)
=
0
f(x) = 0
f
(
x
)
=
0
and
f
(
f
(
x
)
)
=
0
f(f(x)) = 0
f
(
f
(
x
))
=
0
have the same non-empty sets of real roots.
algebra
trigonometry