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UPSC 2015 CDS I Math Paper
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© examsnet.com
Question : 3
Total: 100
For what value of k is (x-5) a factor of
x
3
−
3
x
2
+
k
x
−
10
?
[2015 CDS-I]
-8
4
2
1
Validate
Solution:
Remember:
If (x – a) is a factor of polynomialf(x), then put x = a in the equation f(x) = 0 and solve f(a) = 0.
Let
f
(
x
)
=
x
3
−
3
x
2
+
k
x
−
10
(
x
−
5
)
is a factor of f(x),then
f
(
5
)
=
0
∴
5
3
−
3
×
5
2
+
5
k
−
10
=
0
⇒
5
k
+
40
=
0
⇒
k
=
−
8
© examsnet.com
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