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UPSC NDA Math Model Paper 1
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© examsnet.com
Question : 61
Total: 120
Which of the following is a polynomial with roots
0
,
3
,
and
i
?
x
4
−
3
x
3
+
x
2
−
3
x
x
4
−
3
x
3
−
x
2
−
3
x
x
4
+
3
x
3
+
x
2
−
3
x
x
4
−
3
x
3
+
x
2
+
3
x
Validate
Solution:
Since the complex roots always occur in conjugate pairs, the roots of the polynomial are 0, 3, i and -i.
The required polynomial is
(
x
−
0
)
(
x
−
3
)
(
x
−
i
)
(
x
+
i
)
=
x
(
x
−
3
)
(
x
2
−
i
2
)
=
(
x
2
−
3
x
)
(
x
2
+
1
)
.
.
.
.
.
(
i
=
√
−
1
⇒
i
2
=
−
1
)
=
x
4
+
x
2
−
3
x
3
−
3
x
=
x
4
−
3
x
3
+
x
2
−
3
x
© examsnet.com
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