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AP EAPCET 23-Aug-2021 Shift 2 Paper
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© examsnet.com
Question : 11
Total: 160
Let
ω
=
cis
(
2
π
3
)
=
cos
(
2
π
3
)
+
i
sin
(
2
π
3
)
and
f
(
x
)
=
x
7
−
2
x
4
−
4
x
3
+
8
. Which of the following option is correct?
{
2
1
2
,
2
1
3
,
ω
,
2
1
3
ω
}
is a subset of the solution set of
f
(
x
)
.
{
2
1
2
,
−
2
1
3
,
2
1
3
ω
2
,
2
1
2
i
}
is a subset of the solution set of
f
(
x
)
.
{
2
1
3
,
2
1
2
,
−
2
1
2
i
,
2
1
3
ω
2
}
is not a subset of the solution set of
f
(
x
)
.
{
2
1
3
,
2
1
3
ω
,
2
1
2
i
,
−
2
1
2
}
is a subset of the solution set of
f
(
x
)
.
Validate
Solution:
Given,
ω
=
cis
(
2
π
3
)
=
cos
(
2
π
3
)
+
i
sin
(
2
π
3
)
f
(
x
)
=
x
7
−
2
x
4
−
4
x
3
+
8
ω
=
−
1
2
+
i
√
3
2
=
−
1
+
i
√
3
2
f
(
x
)
=
x
7
−
2
x
4
−
4
x
3
+
8
⇒
x
4
(
x
3
−
2
)
−
4
(
x
3
−
2
)
f
(
x
)
=
(
x
3
−
2
)
(
x
4
−
4
)
For finding solution, let
f
(
x
)
=
0
(
x
3
−
2
)
(
x
4
−
4
)
=
0
⇒
x
3
−
2
=
0
...(i)
or
x
4
−
4
=
0
x
=
2
1
3
or
x
4
=
4
x
2
=
±
2
When
x
2
=
2
and when
x
2
=
−
2
x
=
±
2
1
2
and
x
=
2
1
2
i
From Eq. (i), we get
x
3
−
2
=
0
x
3
−
(
3
√
2
)
3
=
0
⇒
(
x
−
2
1
3
)
(
x
2
+
2
2
3
+
2
1
3
x
)
=
0
⇒
x
−
2
1
3
=
0
or
x
2
+
2
1
3
x
+
2
2
3
=
0
⇒
x
=
2
t
3
x
=
−
2
2
3
±
√
2
2
∕
3
−
4
.
2
2
∕
3
2
x
=
−
2
1
∕
3
±
2
1
∕
3
√
3
i
2
x
=
2
1
∕
3
(
−
1
+
√
3
i
)
2
=
2
1
∕
3
ω
∴ Solution set
=
{
2
1
∕
3
,
2
1
∕
3
ω
,
2
1
∕
2
i
,
−
2
1
∕
2
}
.
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