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UPSC 2017 CDS II Math Paper
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© examsnet.com
Question : 22
Total: 100
If the roots of the equation
a
(
b
−
c
)
x
2
+
b
(
c
−
a
)
x
+
c
(
a
−
b
)
=
0
are equal, then which one of the following is correct ?
[2017 CDS-II]
2
b
=
a
+
c
b
2
=
a
c
2
b
=
1
a
+
1
c
1
b
=
1
a
+
1
c
Validate
Solution:
a
(
b
−
c
)
+
b
(
c
−
a
)
+
c
(
a
−
b
)
=
0
Therefore, x = 1 is the root of the given equation.
It is given that roots of the equation are equal. So, both the roots of the equation are 1.
Therefore, product of the roots = 1
⇒
c
(
a
−
b
)
a
(
b
b
−
c
)
=
1
⇒
c
a
−
b
c
=
a
b
−
a
c
⇒
2
c
a
=
b
c
+
a
b
⇒
2
b
=
1
a
+
1
c
© examsnet.com
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