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Mathematics
Mathematics
Problem
Let
f
(
x
)
=
2
x
4
+
a
x
3
+
b
x
2
−
14
x
+
8
f(x)=2x^{4}+ax^{3}+bx^{2}-14x+8
f
(
x
)
=
2
x
4
+
a
x
3
+
b
x
2
−
14
x
+
8
. If both
(
x
−
1
)
(x-1)
(
x
−
1
)
and
(
x
+
2
)
(x+2)
(
x
+
2
)
are factors of
f
(
x
)
f(x)
f
(
x
)
, calculate the values of
a
a
a
and
b
b
b
.
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