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IIT JEE Advanced 2009 Paper 2
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© examsnet.com
Question : 56
Total: 57
Let p(x) be a polynomial of degree 4 having extremum at x = 1, 2 and
lim
x
→
0
(
1
+
p
(
x
)
x
2
)
= 2. Then, the value of p(2) is _____.
Your Answer:
Validate
Solution:
Let us consider
P (x) =
a
x
4
+
b
x
+
c
x
2
+
d
x
+
e
P' (1) = P' (2) = 0
lim
x
→
0
(
x
2
+
P
(
x
)
x
2
)
= 2
⇒ P(0) = 0⇒e = 0
lim
x
→
0
(
2
x
+
P
′
(
x
)
2
x
)
= 2
⇒ P' 90) = 0 ⇒ d = 0
lim
x
→
0
(
2
+
P
"
(
x
)
2
)
= 2
⇒ c = 1
On solving, we get a = 1/4, b = − 1. Thus,
P (x) =
x
4
4
−
x
3
+
x
2
⇒ P (2) = 0
© examsnet.com
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