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JEE Main Math Class 12 Application of Derivatives Part 2 Questions
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Question : 22
Total: 100
The number of distinct real roots of the equation
x
7
−
7
x
−
2
=
0
is
[24-Jun-2022-Shift-2]
5
7
1
3
Validate
Solution:
👈: Video Solution
Given equation
x
7
−
7
x
−
2
=
0
Let
f
(
x
)
=
x
7
−
7
x
−
2
f
′
(
x
)
=
7
x
6
−
7
=
7
(
x
6
−
1
)
and
f
′
(
x
)
=
0
⇒
x
=
+
1
and
f
(
−
1
)
=
−
1
+
7
−
2
=
5
>
0
f
(
1
)
=
1
−
7
−
2
=
−
8
<
0
So, roughly sketch of
f
(
x
)
will be
So, number of real roots of
f
(
x
)
=
0
and 3
© examsnet.com
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