A) -7
B) 7
C) -1
D) \[-6-{{3}^{(7/3)}}\]
Correct Answer: B
Solution :
Let \[f(x)={{(x+1)}^{7}}+{{(3x+k)}^{3}}\] Since,\[(x+2)\] is a factor of\[f(x).\]Therefore, by factor theorem,\[f(-2)=0\] \[\Rightarrow \]\[{{(-2+1)}^{7}}+(3x(-2)+k)3=0\] \[\Rightarrow \]\[{{(-1)}^{7}}+{{(-6+k)}^{3}}=0\Rightarrow {{(-6+k)}^{3}}=1\] \[\Rightarrow \]\[-6+k=1\Rightarrow k=7\]You need to login to perform this action.
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