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UPSC 2013 CDS 2 Math Paper
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© examsnet.com
Question : 7
Total: 100
Consider the following statements:
1.
x
+
3
is the factor of
x
3
+
2
x
2
+
3
x
+
8
2.
x
–
2
is the factor of
x
3
+
2
x
2
+
3
x
+
8
.
Which of the statements given above is/are correct?
[2013 CDS-II]
1 only
2 only
Both 1 and 2
Neither 1 nor 2
Validate
Solution:
Let f(x)=x^3+2x^2+3x+8
f
(
−
3
)
=
(
−
3
)
3
+
2
(
−
3
)
2
+
3
(
−
3
)
+
8
=
−
27
+
18
−
9
+
8
≠
0
So,
(
x
+
3
)
is not a factor of f(x)
Hence statement 1 is incorrect.
Also,
f
(
2
)
=
2
3
+
2
(
2
)
2
+
3
(
2
)
+
8
≠
0
So,
(
x
–
2
)
is not a factor of f(x).
Hence statement 2 is incorrect.
© examsnet.com
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