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TS EAMCET 18-July-2022 Shift 2 Solved Paper
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© examsnet.com
Question : 12
Total: 160
If
α
,
β
,
γ
are the roots of the equation
x
3
+
x
2
+
x
+
r
=
0
and
α
3
+
β
3
+
γ
3
=
5
, then
r
=
−
1
2
1
-1
1
2
Validate
Solution:
👈: Video Solution
x
3
+
x
2
+
x
+
r
=
0
α
+
β
+
γ
=
−
1
,
α
β
+
β
γ
+
γ
α
=
1
,
α
β
γ
=
−
r
α
3
+
β
3
+
γ
3
=
5
.
⇒
[
α
3
+
β
3
+
γ
3
−
3
α
β
γ
]
+
3
α
β
γ
=
5
⇒
[
(
α
+
β
+
γ
)
(
α
2
+
β
2
+
γ
2
−
α
β
−
β
γ
−
γ
α
)
]
+
3
(
−
r
)
=
5
.
⇒
(
−
1
)
[
(
α
2
+
β
2
+
γ
2
+
2
α
β
+
2
β
γ
+
2
γ
α
)
.
−
3
α
β
−
3
β
γ
−
3
γ
α
]
−
3
r
=
5
⇒
−
{
(
α
+
β
+
γ
)
2
−
3
(
α
β
+
β
γ
+
γ
α
)
}
−
3
r
=
5
⇒
−
{
(
−
1
)
2
−
3
(
1
)
}
−
3
r
=
5
⇒
2
−
3
r
=
5
∴
r
=
−
1
© examsnet.com
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