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Mathematics
Mathematics
Problem
For the family of functions
F
a
(
x
)
=
x
3
−
2
a
x
+
a
F_a(x)=x^{3}-2a x+a
F
a
(
x
)
=
x
3
−
2
a
x
+
a
defined on the interval
[
0
,
2
]
[0,2]
[
0
,
2
]
, determine all real numbers
a
a
a
for which the equation
F
a
(
x
)
=
0
F_a(x)=0
F
a
(
x
)
=
0
has at least one solution in
[
0
,
2
]
[0,2]
[
0
,
2
]
. State your reasoning clearly.
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