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Mathematics
Problem
If
f
(
x
)
=
x
3
−
9
a
x
2
+
15
a
2
x
+
30
f(x) = x^3 - 9ax^2 + 15a^2x + 30
f
(
x
)
=
x
3
−
9
a
x
2
+
15
a
2
x
+
30
,
(
a
>
0
)
(a > 0)
(
a
>
0
)
has its maximum value at
x
=
α
x = \alpha
x
=
α
and its local minimum value at
x
=
β
x = \beta
x
=
β
such that
5
α
2
=
2
β
5\alpha^2 = 2\beta
5
α
2
=
2
β
, then possible value of 'a' is divisible by: (A) 2 (B) 3 (C) 5 (D) 7
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