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Byju's Answer
Standard IX
Mathematics
Zeroes of a Polynomial
Solve the giv...
Question
Solve the given quadratic equation by factorization method
x
2
−
2
a
x
+
a
2
−
b
2
=
0
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Solution
We have
x
2
−
2
a
x
+
a
2
−
b
2
=
0
Here factors of constant term
(
a
2
−
b
2
)
are
(
a
−
b
)
and
(
a
+
b
)
Also, Coefficient of the middle term
=
−
2
a
=
−
[
(
a
−
b
)
+
(
a
+
b
)
]
∴
x
2
−
2
a
x
+
a
2
−
b
2
=
0
⇒
x
2
−
[
(
a
−
b
)
+
(
a
+
b
)
]
x
+
(
a
−
b
)
(
a
+
b
)
=
0
⇒
x
2
−
(
a
−
b
)
x
−
(
a
+
b
)
x
+
(
a
−
b
)
(
a
+
b
)
=
0
⇒
{
x
2
−
(
a
−
b
)
x
}
−
{
(
a
+
b
)
x
−
(
a
−
b
)
(
a
+
b
)
}
=
0
⇒
x
{
x
−
(
a
−
b
)
}
−
(
a
+
b
)
{
x
−
(
a
−
b
)
}
=
0
⇒
x
−
(
a
−
b
)
=
0
o
r
x
−
(
a
+
b
)
=
0
⇒
x
=
a
−
b
o
r
x
=
a
+
b
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