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Byju's Answer
Standard XII
Mathematics
Common Roots
A value of b ...
Question
A value of b for which the equations
x
2
+
b
x
−
1
=
0
and
x
2
+
x
+
b
=
0
have one root in common, is?
A
√
2
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B
√
3
i
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C
i
√
5
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D
−
i
√
2
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Solution
The correct option is
B
√
3
i
Given:
x
2
+
b
x
−
1
=
0
and
x
2
+
x
+
b
=
0
have one common root.
Let the common root be
α
⇒
α
2
+
b
α
−
1
=
0
and
α
2
+
α
+
b
=
0
⇒
α
2
−
1
−
b
2
=
−
α
−
1
−
b
=
1
b
−
1
⇒
α
=
b
+
1
b
−
1
,
α
α
=
−
1
+
b
2
1
+
b
and
α
2
=
b
2
+
1
1
−
b
⇒
(
1
+
b
)
2
=
(
1
+
b
2
)
(
1
−
b
)
⇒
b
2
=
−
3
or
b
=
√
3
i
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