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IIT JEE Advanced 2011 Paper 2
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© examsnet.com
Question : 56
Total: 60
The number of distinct real roots of
x
4
−
4
x
3
+
12
x
2
+
x
−
1
=
0
is _____.
Your Answer:
Validate
Solution:
Let f (x) =
x
4
−
4
x
3
+
12
x
2
+
x
−
1
= 0.
f' (x) =
4
x
3
−
12
x
2
+
24
x
+
1
=
4
(
x
3
−
3
x
2
+
6
x
)
+
1
f" (x) =
12
x
2
−
24
x
+
24
=
12
(
x
2
−
2
x
+
2
)
f ′′(x) has 0 real roots.
f (x) has maximum two distinct real roots as f (0) = −1.
© examsnet.com
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