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JEE Advanced 2012 Paper 2 Mathematics Q5
Mathematics
Problem
Let
α
(
a
)
\alpha(a)
α
(
a
)
and
β
(
a
)
\beta(a)
β
(
a
)
be the roots of the equation
(
1
+
a
3
−
1
)
x
2
+
(
1
+
a
−
1
)
x
+
(
1
+
a
6
−
1
)
=
0
\left(\sqrt[3]{1+a}-1\right)x^2+\left(\sqrt{1+a}-1\right)x+\left(\sqrt[6]{1+a}-1\right)=0
(
3
1
+
a
−
1
)
x
2
+
(
1
+
a
−
1
)
x
+
(
6
1
+
a
−
1
)
=
0
, where
a
>
−
1
a>-1
a
>
−
1
. Then
lim
a
→
0
+
α
(
a
)
\lim_{a\to0^+}\alpha(a)
lim
a
→
0
+
α
(
a
)
and
lim
a
→
0
+
β
(
a
)
\lim_{a\to0^+}\beta(a)
lim
a
→
0
+
β
(
a
)
are
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