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Test Index
JEE Main Math Class 11 Complex Numbers and Quadratic Equations Part 2 Questions
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© examsnet.com
Question : 2
Total: 100
The sum of the roots of the equation
x
+
1
−
2
log
2
(
3
+
2
x
)
+
2
log
4
(
10
−
2
−
x
)
=
0
is
[2021, 31 Aug. Shift-II]
log
2
14
log
2
11
log
2
12
log
2
13
Validate
Solution:
x
+
1
−
2
log
2
(
3
+
2
x
)
+
2
log
4
(
10
−
2
−
x
)
=
0
⇒
x
+
1
−
2
log
2
(
3
+
2
x
)
+
log
2
(
10
⋅
2
x
−
1
2
x
)
=
0
⇒
x
+
1
−
2
log
2
(
3
+
2
x
)
+
log
2
(
10
⋅
2
x
−
1
)
⇒
1
+
log
2
(
10
⋅
2
x
−
1
(
3
+
2
x
)
2
)
=
0
⇒
10
⋅
2
x
−
1
9
+
(
2
x
)
2
+
6
⋅
2
x
=
1
2
⇒
(
2
x
)
2
−
14
⋅
2
x
+
11
=
0
Let
2
x
=
y
⇒
y
2
−
14
y
+
11
=
0
Let
2
x
=
y
⇒
y
2
−
14
y
+
11
=
0
y
=
14
±
√
152
2
=
7
±
√
152
2
y
1
=
7
+
√
152
2
,
y
2
=
7
−
√
152
2
⇒
2
x
1
=
7
+
√
152
2
,
2
x
2
=
7
−
√
152
2
⇒
x
1
=
log
2
(
7
+
√
152
2
)
x
2
=
log
2
(
7
−
√
152
2
)
∴
Sum of roots
=
x
1
+
x
2
=
log
2
(
49
−
152
4
)
=
log
2
11
© examsnet.com
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