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NDA Math Complex Numbers
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© examsnet.com
Question : 50
Total: 66
(
x
3
−
1
)
can be factorised as
Where
ω
is one of the cube roots of unity.
[NDA I 2015]
(
x
−
1
)
(
x
−
ω
)
(
x
+
ω
2
)
(
x
−
1
)
(
x
−
ω
)
(
x
−
ω
2
)
(
x
−
1
)
(
x
+
ω
)
(
x
+
ω
2
)
(
x
−
1
)
(
x
+
ω
)
(
x
+
ω
2
)
Validate
Solution:
Consider the following equation and its roots
x
2
+
x
+
1
=
=
0
→
x
=
⍵
,
⍵
2
∴
x
2
+
x
+
1
=
(
x
−
⍵
)
(
x
−
⍵
2
)
....(1)
Now consider the given question
(
x
3
−
1
)
=
(
x
−
1
)
(
x
2
+
x
+
1
)
From (i) we get
(
x
−
1
)
(
x
2
+
x
+
1
)
=
(
x
−
1
)
(
x
−
⍵
)
(
x
−
⍵
2
)
© examsnet.com
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