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Mathematics
Problem
The set of all values of
k
>
−
1
k > -1
k
>
−
1
, for which the equation
(
3
x
2
+
4
x
+
3
)
2
−
(
k
+
1
)
(
3
x
2
+
4
x
+
3
)
(
3
x
2
+
4
x
+
2
)
+
k
(
3
x
2
+
4
x
+
2
)
2
=
0
(3x^2 + 4x + 3)^2 - (k + 1)(3x^2 + 4x + 3)(3x^2 + 4x + 2) + k(3x^2 + 4x + 2)^2 = 0
(
3
x
2
+
4
x
+
3
)
2
−
(
k
+
1
)
(
3
x
2
+
4
x
+
3
)
(
3
x
2
+
4
x
+
2
)
+
k
(
3
x
2
+
4
x
+
2
)
2
=
0
has real roots, is: (A)
(
1
,
5
2
]
\left(1, \frac{5}{2}\right]
(
1
,
2
5
]
(B)
[
2
,
3
)
[2, 3)
[
2
,
3
)
(C)
[
−
1
2
,
1
)
\left[-\frac{1}{2}, 1\right)
[
−
2
1
,
1
)
(D)
(
1
2
,
3
2
]
−
{
1
}
\left(\frac{1}{2}, \frac{3}{2}\right] - \{1\}
(
2
1
,
2
3
]
−
{
1
}
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