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Byju's Answer
Standard IX
Mathematics
Geometric Progression
If the roots ...
Question
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 =
A
2
b
=
a
c
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B
b
2
=
a
c
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C
b
=
2
a
c
a
+
c
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D
b
=
a
c
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Solution
The correct option is
B
b
2
=
a
c
(
a
2
+
b
2
)
x
2
−
2
b
(
a
+
c
)
x
+
(
b
2
+
c
2
)
=
0
Roots are real and equal
∴
D
=
0
D
=
b
2
−
4
a
c
=
0
⇒
[
−
2
b
(
a
+
c
)
]
2
−
4
(
a
2
+
b
2
)
(
b
2
+
c
2
)
=
0
⇒
b
2
(
a
2
+
c
2
+
2
a
c
)
−
(
a
2
b
2
+
a
2
c
2
+
b
4
+
c
2
c
2
)
=
0
⇒
b
2
a
2
+
b
2
c
2
+
2
a
c
b
2
−
a
2
b
2
−
a
2
c
2
−
b
4
−
b
2
c
2
=
0
⇒
2
a
c
b
2
−
a
2
c
2
−
2
a
c
b
2
=
0
⇒
(
b
2
−
a
c
)
2
=
0
⇒
b
2
=
a
c
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0
Similar questions
Q.
If the roots of the equations
a
2
+
b
2
x
2
-
2
b
a
+
c
x
+
b
2
+
c
2
=
0
are equal, then
(a) 2b = a + c
(b) b
2
= ac
(c)
b
=
2
a
c
a
+
c
(d) b = ac