A) 4
B) \[-4\]
C) 2
D) 0
Correct Answer: B
Solution :
The expression \[3{{x}^{3}}-k{{x}^{2}}+4x+16\]is divisible by \[x-\frac{k}{2}\]. Then, \[x=\frac{k}{2}\] satisfy the equation \[\Rightarrow \] \[3{{\left( \frac{k}{2} \right)}^{3}}-k{{\left( \frac{k}{2} \right)}^{2}}+4\left( \frac{k}{2} \right)+16=0\] \[\Rightarrow \] \[\frac{3{{k}^{3}}-2{{k}^{3}}+16k+128}{8}=0\] \[\Rightarrow \] \[{{k}^{3}}+16k+128=0\] \[\Rightarrow \] \[(k+4)\,({{k}^{2}}-4k+32)=0\] \[\Rightarrow \] \[k+4=0\] \[\Rightarrow \] \[k=-4\]
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