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Poland - Second Round
1987 Poland - Second Round
4
4
Part of
1987 Poland - Second Round
Problems
(1)
2 diff. common roots for x^4 + 2ax^2 + 4bx + a^2 and x^3 + ax - b
Source: Polish MO Recond Round 1987 p4
9/9/2024
Determine all pairs of real numbers
a
,
b
a, b
a
,
b
for which the polynomials
x
4
+
2
a
x
2
+
4
b
x
+
a
2
x^4 + 2ax^2 + 4bx + a^2
x
4
+
2
a
x
2
+
4
b
x
+
a
2
and
x
3
+
a
x
ā
b
x^3 + ax - b
x
3
+
a
x
ā
b
have two different common real roots.
algebra
polynomial