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National and Regional Contests
India Contests
Postal Coaching
2005 Postal Coaching
25
25
Part of
2005 Postal Coaching
Problems
(1)
A cubic
Source: Indian Postal Coaching 2005
10/27/2005
Find all pairs of cubic equations
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
and
x
3
+
b
x
2
+
a
x
+
c
=
0
x^3 +bx^2 + ax +c = 0
x
3
+
b
x
2
+
a
x
+
c
=
0
where
a
,
b
,
c
a,b,c
a
,
b
,
c
are integers, such that each equation has three integer roots and both the equations have exactly one common root.
algebra unsolved
algebra