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4
( a/4)^4 = (b/3)^3 if x^4 + ax + b = 0 has two equal roots,
( a/4)^4 = (b/3)^3 if x^4 + ax + b = 0 has two equal roots,
Source: Polish MO Finals 1960 p4
August 30, 2024
algebra
polynomial
Problem Statement
Prove that if the equation
x
4
+
a
x
+
b
=
0
x^4 + ax + b = 0
x
4
+
a
x
+
b
=
0
has two equal roots, then
(
a
4
)
4
=
(
b
3
)
3
.
\left( \frac{a}{4} \right)^4 =\left( \frac{b}{3} \right)^3.
(
4
a
)
4
=
(
3
b
)
3
.
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