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Mathematics
Mathematics
Problem
Let
f
m
(
x
)
=
x
3
−
5
x
+
m
f_m(x)=x^{3}-5x+m
f
m
(
x
)
=
x
3
−
5
x
+
m
, where
m
m
m
is a real parameter. Determine all real values of
m
m
m
for which the equation
f
m
(
x
)
=
0
f_m(x)=0
f
m
(
x
)
=
0
has at least one real solution in each of the intervals
(
0
,
1
)
(0,1)
(
0
,
1
)
and
(
2
,
3
)
(2,3)
(
2
,
3
)
.
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