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UPSC NDA Math Model Paper 7
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© examsnet.com
Question : 7
Total: 120
If the roots of the equation
(
a
2
+
b
2
)
x
2
−
2
b
(
a
+
c
)
x
+
(
b
2
+
c
2
)
=
0
are equal, then which one of the following is correct?
2b = a + c
b
2
=
a
c
b + c = 2a
b = ac
Validate
Solution:
Given equation is
(
a
2
+
b
2
)
x
2
−
2
b
(
a
+
c
)
x
+
(
b
2
+
c
2
)
=
0
The roots of the equations are equal
⇒
4
b
2
(
a
+
c
)
2
−
4
(
a
2
+
b
2
)
(
b
2
+
c
2
)
=
0
⇒
4
b
2
(
a
2
+
2
a
c
+
c
2
)
−
4
(
a
2
b
2
+
a
2
c
2
+
b
4
+
b
2
c
2
)
=
0
⇒
(
4
b
2
a
2
+
8
b
2
a
c
+
4
b
2
c
2
)
−
(
4
a
2
b
2
+
4
a
2
c
2
+
4
b
4
+
4
b
2
c
2
)
=
0
⇒
8
b
2
a
c
−
4
a
2
c
2
−
4
b
4
=
0
⇒
−
4
(
b
2
−
a
c
)
2
=
0
∴
b
2
=
a
c
© examsnet.com
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