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Putnam
1978 Putnam
B5
Putnam 1978 B5
Putnam 1978 B5
Source: Putnam 1978
May 2, 2022
Putnam
algebra
polynomial
Problem Statement
Find the largest
a
a
a
for which there exists a polynomial
P
(
x
)
=
a
x
4
+
b
x
3
+
c
x
2
+
d
x
+
e
P(x) =a x^4 +bx^3 +cx^2 +dx +e
P
(
x
)
=
a
x
4
+
b
x
3
+
c
x
2
+
d
x
+
e
with real coefficients which satisfies
0
≤
P
(
x
)
≤
1
0\leq P(x) \leq 1
0
≤
P
(
x
)
≤
1
for
−
1
≤
x
≤
1.
-1 \leq x \leq 1.
−
1
≤
x
≤
1.
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