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TS EAMCET 19-July-2022 Shift 2 Solved Paper
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© examsnet.com
Question : 13
Total: 160
If
α
,
β
,
γ
are the roots of the equation
x
3
+
4
x
2
−
9
x
−
36
=
0
such that
α
+
β
=
0
, then
α
2
+
2
β
2
+
3
γ
2
=
75
61
34
27
Validate
Solution:
Given,
α
,
β
and
γ
are the roots of equation
x
3
+
4
x
2
−
9
x
−
36
=
0
and
α
+
β
=
0
∴
α
+
β
+
γ
=
−
4
⇒
γ
=
−
4
α
β
+
β
γ
+
γ
α
=
−
9
⇒
α
β
+
γ
(
α
+
β
)
=
−
9
⇒
α
β
=
−
9
α
(
−
α
)
=
−
9
[
∵
α
+
β
=
0
]
−
α
2
=
−
9
⇒
α
2
=
3
If
α
=
−
3
, then
β
=
3
and if
α
=
3
, then
β
=
−
3
Now,
α
2
+
2
β
2
+
3
γ
2
=
9
+
2
×
9
+
3
×
16
=
27
+
48
=
75
© examsnet.com
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