The number of real zeroes of x4−1=0 is
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Answer:
Real roots of the equation are
1
and
−
1
and complex roots are
i
and
−
i
.
Explanation:
As
x
4
=
1
,
(
x
4
−
1
)
=
0
Using
a
2
−
b
2
=
(
a
+
b
)
(
a
−
b
)
above is equal to
(
x
2
+
1
)
(
x
2
−
1
)
=
0
or
(
x
2
−
i
2
)
(
x
2
−
1
)
, (as
i
2
=
−
1
)
or
(
x
+
i
)
(
x
−
i
)
(
x
+
1
)
(
x
−
1
)
=
0
Hence real roots of the equation are
1
and
−
1
and complex roots are
i
and
−
i
.
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