$\begin{array}{1 1}(A)\;4,24&(B)\;-4,-24\\(C)\;4,-24&(D)\;-4,24\end{array} $

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Let the roots be $\alpha,\alpha^2$

$\alpha+\alpha^2=\large\frac{6}{8}$$\Rightarrow \alpha(1+\alpha)=\large\frac{3}{4}$$\Rightarrow \alpha=\large\frac{-3}{2},\frac{1}{2}$

$\alpha^3=-\large\frac{(k+3)}{8}$

$\Rightarrow -\large\frac{(k+3)}{8}=\frac{-27}{8},\frac{1}{8}$

$\Rightarrow -(k+3)=-27,1$

$\Rightarrow k+3=27,-1$

$\Rightarrow k=24,-4$

Hence (D) is the correct answer.

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