A) 144
B) 100
C) \[-81~~\]
D) \[-300\]
Correct Answer: D
Solution :
Given equation is \[81{{x}^{2}}+kx+256=0\] ...(i) Let \[\alpha \]and \[{{\alpha }^{3}}\]are the roots of the equation (i) \[\therefore \]\[\alpha .{{\alpha }^{3}}=\frac{256}{81}\Rightarrow \alpha =\pm \frac{4}{3}\] Now,\[\alpha +{{\alpha }^{3}}=-\frac{k}{81}\] \[\Rightarrow \]\[\pm \frac{4}{3}\pm \frac{64}{27}=-\frac{k}{81}\] \[\Rightarrow \]\[k=\pm \frac{100}{27}\times 81=\pm 300\]
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