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Putnam
1953 Putnam
B5
Putnam 1953 B5
Putnam 1953 B5
Source: Putnam 1953
July 16, 2022
Putnam
polynomial
Root
Problem Statement
Show that the roots of
x
4
+
a
x
3
+
b
x
2
+
c
x
+
d
x^4 +ax^3 +bx^2 +cx +d
x
4
+
a
x
3
+
b
x
2
+
c
x
+
d
, if suitably numbered, satisfy the relation
r
1
r
2
=
r
3
r
4
,
\frac{r_1 }{r_2 } = \frac{ r_3 }{r _4},
r
2
r
1
=
r
4
r
3
,
provided
a
2
d
=
c
2
≠
0.
a^2 d=c^2 \ne 0.
a
2
d
=
c
2
=
0.
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