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Contests
National and Regional Contests
Vietnam Contests
Hanoi Open Mathematics Competition
2007 Hanoi Open Mathematics Competitions
6
HOMC (Vietnam)
HOMC (Vietnam)
Source:
January 28, 2016
algebra
Problem Statement
Let
P
(
x
)
=
x
3
+
a
x
2
+
b
x
+
1
P(x) = x^3 + ax^2 + bx + 1
P
(
x
)
=
x
3
+
a
x
2
+
b
x
+
1
and
∣
P
(
x
)
∣
≤
1
|P(x)| \leq 1
∣
P
(
x
)
∣
≤
1
for all x such that
∣
x
∣
≤
1
|x| \leq 1
∣
x
∣
≤
1
. Prove that
∣
a
∣
+
∣
b
∣
≤
5
|a| + |b| \leq 5
∣
a
∣
+
∣
b
∣
≤
5
.
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