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Mathematics
Mathematics
Problem
Consider the function
g
(
x
)
=
x
2
+
k
x
−
3
g(x)=x^{2}+kx-3
g
(
x
)
=
x
2
+
k
x
−
3
on the interval
[
1
,
4
]
[1,4]
[
1
,
4
]
, where
k
k
k
is a real parameter. Determine all real values of
k
k
k
for which there exists a number
c
c
c
in
[
1
,
4
]
[1,4]
[
1
,
4
]
satisfying
g
(
c
)
=
0
g(c)=0
g
(
c
)
=
0
.
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