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UPSC 2017 CDS II Math Paper
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© examsnet.com
Question : 24
Total: 100
If k is an integer, then
x
2
+
7
x
−
14
(
k
2
−
7
8
)
=
0
has
[2017 CDS-II]
Both integral roots
At least one integral root
No integral root
Both positive integral roots
Validate
Solution:
x
=
−
7
±
√
49
+
56
(
k
2
−
7
8
)
2
(
x
=
−
b
±
√
D
2
a
)
⇒
x
=
−
7
±
√
56
k
2
2
⇒
x
=
−
7
±
2
√
14
k
2
Thus, the given equation has no integral roots.
© examsnet.com
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