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Byju's Answer
Standard XII
Mathematics
Higher Order Equations
The number of...
Question
The number of common roots of the two equations
x
3
−
x
2
+
x
−
1
=
0
and
x
4
−
1
=
0
is
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Solution
x
3
−
x
2
+
x
−
1
=
0
⇒
(
x
−
1
)
(
x
2
+
1
)
=
0
⇒
x
=
1
,
i
,
−
i
x
4
−
1
=
0
⇒
(
x
+
1
)
(
x
−
1
)
(
x
2
+
1
)
=
0
⇒
x
=
−
1
,
1
,
i
,
−
i
∴
Number of common roots
=
3
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3
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