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|2a + b| >=4, |ax^2 + bx + c| <=1 for x \in [-1, 1] (HOMC 2016 S Q13)
|2a + b| >=4, |ax^2 + bx + c| <=1 for x \in [-1, 1] (HOMC 2016 S Q13)
Source:
September 8, 2019
algebra
System
inequalities
Problem Statement
Find all triples
(
a
,
b
,
c
)
(a,b,c)
(
a
,
b
,
c
)
of real numbers such that
∣
2
a
+
b
∣
≥
4
|2a + b| \ge 4
∣2
a
+
b
∣
≥
4
and
∣
a
x
2
+
b
x
+
c
∣
≤
1
|ax^2 + bx + c| \le 1
∣
a
x
2
+
b
x
+
c
∣
≤
1
∀
x
∈
[
−
1
,
1
]
\forall x \in [-1, 1]
∀
x
∈
[
−
1
,
1
]
.
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