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Mathematics
Mathematics
Problem
For real numbers
m
m
m
, define
g
m
(
x
)
=
x
2
−
m
x
+
2
g_m(x)=x^{2}-mx+2
g
m
(
x
)
=
x
2
−
m
x
+
2
. Determine all real values of
m
m
m
for which the equation
g
m
(
x
)
=
0
g_m(x)=0
g
m
(
x
)
=
0
has at least one solution in the interval
[
1
,
4
]
[1,4]
[
1
,
4
]
.
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