MathDB
Problems
Contests
National and Regional Contests
Belarus Contests
Belarus Team Selection Test
2024 Belarus Team Selection Test
4.2
4.2
Part of
2024 Belarus Team Selection Test
Problems
(1)
Quadratic polynomial divides [0,1] in two parts
Source: Belarus TST 2024
7/17/2024
Let
f
(
x
)
=
x
2
+
b
x
+
c
f(x)=x^2+bx+c
f
(
x
)
=
x
2
+
b
x
+
c
, where
b
,
c
∈
R
b,c \in \mathbb{R}
b
,
c
∈
R
and
b
>
0
b>0
b
>
0
Do there exist disjoint sets
A
A
A
and
B
B
B
, whose union is
[
0
,
1
]
[0,1]
[
0
,
1
]
and
f
(
A
)
=
B
f(A)=B
f
(
A
)
=
B
, where
f
(
X
)
=
{
f
(
x
)
,
x
∈
X
}
f(X)=\{f(x), x \in X\}
f
(
X
)
=
{
f
(
x
)
,
x
∈
X
}
D. Zmiaikou
quadratics
algebra
polynomial