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1940 Putnam
B5
B5
Part of
1940 Putnam
Problems
(1)
a, b,c rational roots of x^3+ax^2 + bx + c = 0
Source: Singapore Open Math Olympiad 1995 2nd Round p1 SMO
4/2/2020
Suppose that the rational numbers
a
,
b
a, b
a
,
b
and
c
c
c
are the roots of the equation
x
3
+
a
x
2
+
b
x
+
c
=
0
x^3+ax^2 + bx + c = 0
x
3
+
a
x
2
+
b
x
+
c
=
0
. Find all such rational numbers
a
,
b
a, b
a
,
b
and
c
c
c
. Justify your answer
polynomial
rational
algebra
roots