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JEE Main Math Class 11 Complex Numbers and Quadratic Equations Part 2 Questions
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© examsnet.com
Question : 4
Total: 100
The set of all values of
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
has real roots, is
[2021, 27 Aug. Shift-II]
(
1
,
5
2
]
[
2
,
3
)
[
−
1
2
,
1
)
(
1
2
,
3
2
]
−
{
1
}
Validate
Solution:
Given,
(
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
Let
y
=
3
x
2
+
4
x
+
2
Then, given equation becomes
(
y
+
1
)
2
−
(
k
+
1
)
y
(
y
+
1
)
+
k
y
2
=
0
⇒
y
2
+
2
y
+
1
−
k
y
2
−
k
y
−
y
2
−
y
+
k
y
2
=
0
⇒
y
+
1
−
k
y
=
0
⇒
y
(
1
−
k
)
=
−
1
⇒
y
=
1
k
−
1
⇒
3
x
2
+
4
x
+
2
−
1
k
−
1
=
0
For real roots,
D
≥
0
⇒
16
−
4
⋅
3
⋅
(
2
−
1
k
−
1
)
≥
0
⇒
−
8
+
12
k
−
1
≥
0
⇒
3
k
−
1
≥
2
⇒
3
−
2
k
+
2
k
−
1
≥
0
⇒
2
k
−
5
k
−
1
≤
0
⇒
k
∈
(
1
,
5
2
]
[
∵
k
≠
1
]
© examsnet.com
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