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Putnam
1958 February Putnam
A1
Putnam 1958 February A1
Putnam 1958 February A1
Source: Putnam 1958 February
July 18, 2022
Putnam
roots
polynomial
Problem Statement
If
a
0
,
a
1
,
…
,
a
n
a_0 , a_1 ,\ldots, a_n
a
0
,
a
1
,
…
,
a
n
are real number satisfying
a
0
1
+
a
1
2
+
…
+
a
n
n
+
1
=
0
,
\frac{a_0 }{1} + \frac{a_1 }{2} + \ldots + \frac{a_n }{n+1}=0,
1
a
0
+
2
a
1
+
…
+
n
+
1
a
n
=
0
,
show that the equation
a
n
x
n
+
…
+
a
1
x
+
a
0
=
0
a_n x^n + \ldots +a_1 x+a_0 =0
a
n
x
n
+
…
+
a
1
x
+
a
0
=
0
has at least one real root.
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