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1980 Poland - Second Round
4
4
Part of
1980 Poland - Second Round
Problems
(1)
ax^3 - ax^2 + 9bx - b has 3 positive roots
Source: Polish MO Recond Round 1980 p4
9/9/2024
Prove that if
a
a
a
and
b
b
b
are real numbers and the polynomial
a
x
3
−
a
x
2
+
9
b
x
−
b
ax^3 - ax^2 + 9bx - b
a
x
3
−
a
x
2
+
9
b
x
−
b
has three positive roots, then they are equal.
algebra
polynomial