For what value of k, (2x – k) is a factor of 2 3 -- 9 2 + x + 12 ?
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Answer:
2x−3) is a factor of p(x)=2x
3
−9x
2
+x+K,
If (2x−3)=0,x=
2
3
If (2x−3) is a factor of p(x) then p(
2
3
)=0
p(x)=2x
3
−9x
2
+x+K,
⇒p(
2
3
)=2(
2
3
)−9(
2
3
)+
2
3
+K=0
⇒2(
8
27
)−9(
4
9
)+
2
3
+K=0
⇒(
4
27
−
4
81
+
2
3
+K=0)×4
27−81+6+4K=0
−48+4K=0
4K=48
So K=12
Step-by-step explanation:
Your welcome!
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