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NDA Math Miscellaneous
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© examsnet.com
Question : 8
Total: 24
Suppose f(x) is such a quadrant expression that it is positive for all real x. If
g
(
x
)
=
f
(
x
)
+
f
’
(
x
)
+
f
’
’
(
x
)
, then for any real x. Then for any real x.
[NDA II 2018]
g
(
x
)
<
0
g
(
x
)
>
0
g
(
x
)
=
0
g
(
x
)
≥
0
Validate
Solution:
Let
f
(
x
)
=
a
x
2
+
b
x
+
c
,
a
>
0
,
b
2
<
4
a
c
(
∵
f
(
x
)
>
0
)
Now,
g
(
x
)
=
a
x
2
+
b
x
+
c
+
2
a
x
+
b
+
2
a
=
a
x
2
+
(
b
+
2
a
)
x
+
2
a
+
b
+
c
Now,
(
b
+
2
a
)
2
−
4
a
(
2
a
+
b
+
c
)
=
b
2
+
4
a
b
+
4
a
2
−
8
a
2
−
4
a
b
−
4
a
c
=
b
2
−
4
a
c
−
8
a
2
<
0
⇒
g
(
x
)
>
0
© examsnet.com
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