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1994 All-Russian Olympiad Regional Round
9.5
cx^5 +bx+a = 0, ax^5 + bx^4 + c = 0 All-Russian MO 1994 Regional (R4) 9.5
cx^5 +bx+a = 0, ax^5 + bx^4 + c = 0 All-Russian MO 1994 Regional (R4) 9.5
Source:
August 26, 2024
algebra
Problem Statement
The equation
a
x
5
+
b
x
4
+
c
=
0
ax^5 + bx^4 + c = 0
a
x
5
+
b
x
4
+
c
=
0
has three distinct roots. Show that so does the equation
c
x
5
+
b
x
+
a
=
0
cx^5 +bx+a = 0
c
x
5
+
b
x
+
a
=
0
.
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