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Assam Mathematics Olympiad
2023 Assam Mathematics Olympiad
15
15
Part of
2023 Assam Mathematics Olympiad
Problems
(1)
Assam Mathematics Olympiad 2023 Category III Q15
Source:
9/11/2024
Let
f
(
x
)
f(x)
f
(
x
)
be a polynomial of degree
3
3
3
with real coefficients satisfying
∣
f
(
x
)
∣
=
12
|f(x)| = 12
∣
f
(
x
)
∣
=
12
for
x
=
1
,
2
,
3
,
5
,
6
,
7
x = 1, 2, 3, 5, 6, 7
x
=
1
,
2
,
3
,
5
,
6
,
7
. Find
∣
f
(
0
)
∣
|f(0)|
∣
f
(
0
)
∣
.