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UPSC NDA 2 2012 Mathematics Paper
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© examsnet.com
Question : 2
Total: 120
If
α
,
β
are the roots of
x
2
+
p
x
−
q
=
0
and
γ
,
δ
are roots of
x
2
−
p
x
+
r
=
0
then what is
(
β
+
γ
)
(
β
+
δ
)
equal to?
p
+
r
p
+
q
q
+
r
p
−
q
Validate
Solution:
∵
α
,
β
are the roots of
x
2
+
p
x
−
q
=
0
∴
α
+
β
=
−
p
and
α
×
β
=
−
q
γ
,
δ
are roots of
x
2
−
p
x
+
r
=
0
∴
γ
+
δ
=
+
p
and
γ
×
δ
=
r
(
β
+
γ
)
(
β
+
δ
)
=
β
2
+
β
δ
+
β
γ
+
δ
γ
=
β
2
+
β
(
δ
+
γ
)
+
r
=
β
2
+
p
β
+
r
=
q
+
r
[
∵
β
.
is the root of
x
2
+
p
x
−
q
=
0
∴
β
2
+
p
β
=
q
]
© examsnet.com
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