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Byju's Answer
Standard IX
Mathematics
Zeroes of a Polynomial
Solve the fol...
Question
Solve the following quadratic equation by factorization :
(
a
+
b
)
2
x
2
−
4
a
b
x
−
(
a
−
b
)
2
=
0
The roots are
1,
−
(
a
−
b
a
+
b
)
2
A
True
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B
False
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Solution
The correct option is
A
True
(
a
+
b
)
2
x
2
−
4
a
b
x
−
(
a
−
b
)
2
=
0
As,
−
(
a
+
b
)
2
+
(
a
−
b
)
2
=
−
a
2
−
b
2
−
2
a
b
+
a
2
+
b
2
−
2
a
b
=
−
4
a
b
⇒
(
a
+
b
)
2
x
2
−
(
a
+
b
)
2
x
+
(
a
−
b
)
2
x
−
(
a
−
b
)
2
=
0
⇒
(
a
+
b
)
2
x
[
x
−
1
]
+
(
a
−
b
)
2
[
x
−
1
]
=
0
⇒
(
x
−
1
)
[
(
a
+
b
)
2
x
+
(
a
−
b
)
2
]
=
0
⇒
x
−
1
=
0
and
(
a
+
b
)
2
x
+
(
a
−
b
)
2
=
0
⇒
x
=
1
and
x
=
−
(
a
−
b
)
2
(
a
+
b
)
2
∴
x
=
1
and
x
=
−
(
a
−
b
a
+
b
)
2
∴
We can see, given roots in question are correct.
Suggest Corrections
1
Similar questions
Q.
Solve the following quadratic equations by factorization:
a
+
b
2
x
2
-
4
a
b
x
-
a
-
b
2
=
0