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UPSC 2017 CDS II Math Paper
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© examsnet.com
Question : 1
Total: 100
What is the value of α(α≠0) for which
x
2
−
5
x
+
α
and
x
2
−
7
x
+
2
α
have a common factor ?
[2017 CDS-II]
6
4
3
2
Validate
Solution:
Let x = a be the common root of
x
2
−
5
x
+
α
and
x
2
−
7
x
+
2
α
∴
a
2
−
5
a
+
α
=
0
....(1)
a
2
−
7
a
+
2
α
=
0
......(2)
Subtracting (2) from (1), we get
2
a
−
α
=
0
⇒
a
=
α
2
∴
(
α
2
)
2
−
5
(
α
2
)
+
α
=
0
⇒
α
2
4
−
3
α
2
=
0
⇒
α
2
(
α
2
−
3
)
=
0
⇒
α
2
−
3
=
0
(α ≠ 0)
⇒
α
=
6
© examsnet.com
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