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Byju's Answer
Standard XI
Mathematics
Common Roots
If the equati...
Question
If the equations
x
2
+
a
x
+
b
=
0
and
x
2
+
b
x
+
a
=
0
have a common root and
a
≠
b
,
(
a
,
b
∈
R
)
,
then the value of
|
a
+
b
|
is
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Solution
x
2
+
a
x
+
b
=
0
.
.
.
(
1
)
x
2
+
b
x
+
a
=
0
.
.
.
(
2
)
Let the common root be
α
.
So,
α
will satisfy above two equations.
α
2
+
a
α
+
b
=
0
.
.
.
(
3
)
α
2
+
b
α
+
a
=
0
.
.
.
(
4
)
Subtracting
(
4
)
from
(
3
)
,
we get
α
(
a
−
b
)
=
a
−
b
⇒
α
=
1
(
∵
a
≠
b
)
Put
α
=
1
in eqn
(
1
)
,
we get
a
+
b
=
−
1
⇒
|
a
+
b
|
=
1
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0
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Common Roots
Standard XI Mathematics
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