question_answer

If \[\alpha \] and \[\beta \] are the roots of the given equation \[2\,\sqrt{3}{{x}^{2}}+4x-3\,\sqrt{3},\] then the value of \[\frac{1}{{{\alpha }^{2}}}+\frac{1}{{{\beta }^{2}}}\].

A)  \[\frac{158}{113}\]                              

B)  \[\frac{181\sqrt{3}}{243}\]

C)  \[\frac{280\sqrt{3}}{243}\]

D)  \[\frac{280}{243}\]

E)  None of these