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EAMCET Engineering 2005 Solved Paper
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© examsnet.com
Question : 97
Total: 160
If
α
,
β
,
γ
are the roots of
x
3
+
2
x
2
−
3
x
−
1
=
0
then
α
−
2
+
β
−
2
+
γ
−
2
=
12
13
14
15
Validate
Solution:
Given that,
α
,
β
,
γ
, are the roots of the equation
x
3
+
2
x
2
−
3
x
−
1
=
0
⇒
α
+
β
+
γ
=
−
2
. . . (i)
α
β
+
β
γ
+
γ
α
=
−
3
. . . (ii)
and
α
β
γ
=
1
. . . (iii)
On squaring equation (ii), we get
α
2
β
2
+
β
2
γ
2
+
γ
2
α
2
+
2
α
β
γ
(
α
+
β
+
γ
)
=
9
⇒
α
2
β
2
+
β
2
γ
2
+
γ
2
α
2
=
9
−
2
(1)
(
−
2
)
=
13
Now
α
−
2
+
β
−
2
+
γ
−
2
=
β
2
γ
2
+
γ
2
α
2
+
α
2
β
2
(
α
β
γ
)
2
α
−
2
+
β
−
2
+
γ
−
2
=
13
1
=
13
© examsnet.com
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