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UPSC CDS 2 2018 Math Paper
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© examsnet.com
Question : 16
Total: 100
If a and p are the roots of the equation
a
x
2
+ bx + c = 0, then the value of
1
a
α
+
b
+
1
a
β
+
b
is
[2018 CDS-II]
a
b
c
b
a
c
c
a
b
1
a
b
c
Validate
Solution:
Sum of roots
=
−
b
a
Product of roots
=
c
a
1
a
α
+
b
+
1
a
β
+
b
=
a
β
+
b
+
a
α
+
b
(
a
α
+
b
)
(
a
β
+
b
)
=
a
(
α
+
β
)
+
2
b
[
a
2
α
β
+
a
b
(
α
+
β
)
+
b
2
]
=
a
×
(
−
b
a
)
+
2
b
[
a
2
×
c
a
+
a
b
(
−
b
a
)
+
b
2
]
=
−
b
+
2
b
a
c
−
b
2
+
b
2
=
b
a
c
© examsnet.com
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