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Putnam
1968 Putnam
A5
A5
Part of
1968 Putnam
Problems
(1)
Putnam 1968 A5
Source: Putnam 1968
2/19/2022
Find the smallest possible
α
∈
R
\alpha\in \mathbb{R}
α
∈
R
such that if
P
(
x
)
=
a
x
2
+
b
x
+
c
P(x)=ax^2+bx+c
P
(
x
)
=
a
x
2
+
b
x
+
c
satisfies
∣
P
(
x
)
∣
≤
1
|P(x)|\leq1
∣
P
(
x
)
∣
≤
1
for
x
∈
[
0
,
1
]
x\in [0,1]
x
∈
[
0
,
1
]
, then we also have
∣
P
′
(
0
)
∣
≤
α
|P'(0)|\leq \alpha
∣
P
′
(
0
)
∣
≤
α
.
Putnam
polynomial