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National and Regional Contests
Albania Contests
Albania Team Selection Test
2012 Albania Team Selection Test
3
3
Part of
2012 Albania Team Selection Test
Problems
(1)
Albania IMO TST 2012 equation
Source:
5/18/2013
It is given the equation
x
4
−
2
a
x
3
+
a
(
a
+
1
)
x
2
−
2
a
x
+
a
2
=
0
x^4-2ax^3+a(a+1)x^2-2ax+a^2=0
x
4
−
2
a
x
3
+
a
(
a
+
1
)
x
2
−
2
a
x
+
a
2
=
0
. a) Find the greatest value of
a
a
a
, such that this equation has at least one real root. b) Find all the values of
a
a
a
, such that the equation has at least one real root.
algebra proposed
algebra