A) \[\frac{5}{3}\]
B) \[\frac{8}{3}\]
C) \[\frac{10}{3}\]
D) None of these
Correct Answer: D
Solution :
Let \[\alpha \] and \[{{\alpha }^{2}}\] be the roots of the equation. \[{{x}^{2}}+6mx+64=0\] then, product of roots \[=\frac{c}{a}=\alpha \times {{\alpha }^{2}}={{\alpha }^{3}}=64\] \[\Rightarrow \] \[\alpha =4\] So, the roots are 4 and 16. Sum of the roots \[=\frac{-b}{a}=-6\,m=4=16\] \[\therefore \] \[m=\frac{-20}{6}=\frac{-10}{3}\]
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