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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 : 18
Total: 100
The number of real roots of the equation
e
4
x
−
e
3
x
−
4
e
2
x
−
e
x
+
1
=
0
is equal to .........
[2021, 27 July Shift-II]
Your Answer:
Validate
Solution:
Given equation,
e
4
x
−
e
3
x
−
4
e
2
x
−
e
x
+
1
=
0
Let
e
x
=
t
>
0
t
4
−
t
3
−
4
t
2
−
t
+
1
=
0
⇒
t
2
−
t
−
4
−
1
t
+
1
t
2
=
0
⇒
t
2
+
1
t
2
+
2
−
(
t
+
1
t
)
−
6
=
0
⇒
(
t
+
1
t
)
2
−
(
t
+
1
t
)
−
6
=
0
Let
α
=
t
+
1
t
≥
2
l
c
⇒
α
2
−
α
−
6
=
0
⇒
α
2
−
3
α
+
2
α
−
6
=
0
⇒
α
(
α
−
3
)
+
2
(
α
−
3
)
=
0
⇒
(
α
−
3
)
(
α
+
2
)
=
0
⇒
α
=
3
or
α
=
−
2
(not possible)
⇒
t
+
1
t
=
3
⇒
t
2
−
3
t
+
1
=
0
∴
The number of real roots
=
2
© examsnet.com
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