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Putnam
1953 Putnam
A7
A7
Part of
1953 Putnam
Problems
(1)
Putnam 1953 A7
Source: Putnam 1953
7/16/2022
Assuming that the roots of
x
3
+
p
x
2
+
q
x
+
r
=
0
x^3 +px^2 +qx +r=0
x
3
+
p
x
2
+
q
x
+
r
=
0
are all real and positive, find the relation between
p
,
q
,
r
p,q,r
p
,
q
,
r
which is a necessary and sufficient condition that the roots are the cosines of the angles of a triangle.
Putnam
trigonometry
polynomial
roots