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JEE Main Math Class 11 Complex Numbers and Quadratic Equations Part 2 Questions
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© examsnet.com
Question : 5
Total: 100
The sum of all integral values of
k
(
k
≠
0
)
for which the equation
2
x
−
1
−
1
x
−
2
=
2
k
in
x
has no real roots, is
[2021,26 Aug. Shift-I]
Your Answer:
Validate
Solution:
2
x
−
1
−
1
x
−
2
=
2
k
⇒
x
∈
R
−
{
1
,
2
}
k
(
2
x
−
4
−
x
+
1
)
=
2
(
x
2
−
3
x
+
2
)
k
(
x
−
3
)
=
2
(
x
2
−
3
x
+
2
)
2
x
2
−
(
6
+
k
)
x
+
3
k
+
4
=
0
For no real roots
b
2
−
4
a
c
<
0
∴
(
k
+
6
)
2
−
8
⋅
(
3
k
+
4
)
<
0
⇒
k
2
−
12
k
−
4
<
0
⇒
(
k
−
6
)
2
−
32
<
0
⇒
(
k
−
6
)
2
<
32
⇒
−
4
√
2
<
k
−
6
<
4
√
2
⇒
6
−
4
√
2
<
k
<
6
+
4
√
2
Integral
k
∈
{
1
,
2
,
3
,
4
,
.
.
.
.
.11
}
Sum
=
66
© examsnet.com
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