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Mathematics
Problem
The polynomial
s
(
x
)
=
x
5
+
a
x
3
+
b
x
s(x)=x^{5}+ax^{3}+bx
s
(
x
)
=
x
5
+
a
x
3
+
b
x
satisfies
s
′
(
1
)
=
0
s'(1)=0
s
′
(
1
)
=
0
and
s
′
(
2
)
=
64
s'(2)=64
s
′
(
2
)
=
64
. Determine the values of
a
a
a
and
b
b
b
.
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