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UPSC NDA 2 2019 Mathematics Solved Paper
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© examsnet.com
Question : 6
Total: 120
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?
[NDA II 2019]
a, b and c are in AP
a, b and c are in GP
a, b and c are in HP
a, b and c do not follow any regular pattern
Validate
Solution:
👈: Video Solution
a
(
b
–
c
)
x
2
+
b
(
c
–
a
)
x
+
c
(
a
–
b
)
=
0
Given roots of the equation are equal
x
=
1
∴
α
=
β
=
1
α
+
β
=
2
=
−
b
(
c
−
a
)
a
(
b
−
c
)
and
α
β
=
1
⋅
1
=
1
=
c
(
a
−
b
)
a
(
b
−
c
)
⇒
a
c
−
b
c
=
a
b
−
a
c
⇒
2
a
c
=
b
(
a
+
c
)
⇒
b
=
2
a
c
a
+
c
⇒a, b, c are in H.P.
[
a
x
2
+
b
x
+
c
i
f
a
+
b
+
c
=
0
,
then
x
=
1
one root and
x
=
c
a
]
© examsnet.com
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