The value of k for which (x-2) is a factor of x^3-kx^2+x-2
Answers
Answer:
k=2
Step-by-step explanation:
x=2
x=22^3 -k 2^2+ 2-2
x=22^3 -k 2^2+ 2-28 - 4k +0
x=22^3 -k 2^2+ 2-28 - 4k +08- 4k
x=22^3 -k 2^2+ 2-28 - 4k +08- 4k8=4k
x=22^3 -k 2^2+ 2-28 - 4k +08- 4k8=4k8/4 = k
x=22^3 -k 2^2+ 2-28 - 4k +08- 4k8=4k8/4 = k2=k
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Answer:
Step-by-step explanation:
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Precalculus Topics
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If
x
−
2
is a factor of
x
3
−
k
x
2
+
k
x
+
2
, where
k
is a constant, what is the value of
k
?
Precalculus
1 Answer
sjc
Jun 4, 2017
k
=
5
Explanation:
use the factor theorem which states that
for a polynomial
P
(
x
)
;
[
(
x
−
a
)
is a factor]
⇒
P
(
a
)
=
0
so
P
(
x
)
=
x
3
−
k
x
2
+
k
x
+
2
∵
(
x
−
2
)
is a factor
P
(
2
)
=
2
3
−
k
×
2
2
+
2
k
+
2
=
0
⇒
8
−
4
k
+
2
k
+
2
=
0
10
=
2
k
∴
k
=
5
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