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Soros Olympiad in Mathematics
VII Soros Olympiad 2000 - 01
10.1
(a-1)^2x^4 + (a^2-a) x^3 + 3x - 1 = 0 (VII Soros Olympiad 2000-01 R1 10.1)
(a-1)^2x^4 + (a^2-a) x^3 + 3x - 1 = 0 (VII Soros Olympiad 2000-01 R1 10.1)
Source:
July 28, 2021
algebra
Problem Statement
Find all values of the parameter
a
a
a
for which the equation
(
a
−
1
)
2
x
4
+
(
a
2
−
a
)
x
3
+
3
x
−
1
=
0
(a-1)^2x^4 + (a^2-a) x^3 + 3x - 1 = 0
(
a
−
1
)
2
x
4
+
(
a
2
−
a
)
x
3
+
3
x
−
1
=
0
has a unique solution and for these
a
a
a
solve the equation.
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