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Putnam
1948 Putnam
B1
B1
Part of
1948 Putnam
Problems
(1)
Putnam 1948 B1
Source: Putnam 1948
3/15/2022
Let
f
(
x
)
f(x)
f
(
x
)
be a cubic polynomial with roots
x
1
,
x
2
x_1 , x_2
x
1
,
x
2
and
x
3
.
x_3.
x
3
.
Assume that
f
(
2
x
)
f(2x)
f
(
2
x
)
is divisible by
f
′
(
x
)
f'(x)
f
′
(
x
)
and compute the ratio
x
1
:
x
2
:
x
3
.
x_1 : x_2: x_3 .
x
1
:
x
2
:
x
3
.
Putnam
algebra
polynomial
ratio