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Byju's Answer
Standard XII
Mathematics
Properties of Modulus
Let a ∈ℝ and ...
Question
Let
a
∈
R
and let
f
:
R
→
R
be given by
f
(
x
)
=
x
5
−
5
x
+
a
Then
A
f
(
x
)
has three real roots if
a
>
4
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B
f
(
x
)
has only one real root if
a
>
4
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C
f
(
x
)
has three real roots if
a
<
−
4
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D
f
(
x
)
has three real roots if
−
4
<
a
<
4
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
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Solution
The correct option is
D
f
(
x
)
has three real roots if
−
4
<
a
<
4
f
(
x
)
=
x
5
−
5
x
+
a
⇒
f
′
(
x
)
=
5
x
4
−
5
⇒
f
′
(
x
)
=
5
(
x
4
−
1
)
=
0
⇒
x
=
±
1
⇒
f
′′
(
x
)
=
20
x
3
⇒
f
′′
(
1
)
>
0
,
f
′′
(
−
1
)
<
0
x
=
1
is point of minima,
x
=
−
1
is point of maxima.
f
(
1
)
=
a
−
4
;
f
(
−
1
)
=
a
+
4
When
−
4
<
a
<
4
f
(
x
)
has three real roots.
When
a
>
4
f
(
x
)
has only one root.
When
a
<
−
4
f
(
x
)
has only one root.
Suggest Corrections
6
Similar questions
Q.
Let a
∈
R and let
f
: R
→
R be given by
f
(
x
)
=
x
5
−
5
x
+
a
, then
Q.
Let
a
∈
R
and let
f
:
R
→
R
be given by
f
(
x
)
=
x
5
−
5
x
+
a
. Then
Q.
Let
f
(
x
)
=
{
x
2
∣
∣
cos
π
x
∣
∣
,
x
≠
0
0
,
x
=
0
,
x
∈
R
.
Then
f
is
Q.
Let
f
:
R
→
R
be defined as
f
(
x
)
=
(
|
x
−
1
|
+
|
4
x
−
11
|
)
[
x
2
−
2
x
−
2
]
,
where
[
.
]
denotes the greatest integer function. Then the number of points of discontinuity of
f
(
x
)
in
(
1
2
,
5
2
)
is
Q.
Let
f
be a real valued function, defined on
R
−
{
−
1
,
1
}
and given by
f
(
x
)
=
3
log
e
∣
∣
∣
x
−
1
x
+
1
∣
∣
∣
−
2
x
−
1
.
Then in which of the following intervals, function
f
(
x
)
is increasing ?
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