a zero of x^3+64 is
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Answer:
Explanation:
Notice that this is a sum of cubes, which is factorable as follows:
a
3
+
b
3
=
(
a
+
b
)
(
a
2
−
a
b
+
b
2
)
Thus,
x
3
+
64
is factorable into
x
3
+
4
3
=
(
x
+
4
)
(
x
2
−
4
x
+
16
)
=
0
Now, we have one linear factor and one quadratic factor.
(
x
+
4
)
(
x
2
−
4
x
+
16
)
=
0
We can set each of these equal to
0
individually to find the values of
x
that make the whole expression equal
0
.
x
+
4
=
0
⇒
x
=
−
4
The next requires the quadratic formula.
x
2
−
4
x
+
16
=
0
⇒
x
=
4
±
√
16
−
64
2
⇒
x
=
4
±
4
√
3
i
2
⇒
x
=
2
±
2
√
3
i
Step-by-step explanation:
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