question_answer

If \[\alpha ,\beta \] are the roots of the equation \[l{{x}^{2}}+mx+n=0\], then the equation whose roots are \[{{\alpha }^{3}}\beta \] and \[\alpha {{\beta }^{3}}\] is [MP PET 1997]

A) \[{{l}^{4}}{{x}^{2}}-nl({{m}^{2}}-2nl)x+{{n}^{4}}=0\]

B) \[{{l}^{4}}{{x}^{2}}+nl({{m}^{2}}-2nl)x+{{n}^{4}}=0\]

C) \[{{l}^{4}}{{x}^{2}}+nl({{m}^{2}}-2nl)x-{{n}^{4}}=0\]

D) \[{{l}^{4}}{{x}^{2}}-nl({{m}^{2}}+2nl)x+{{n}^{4}}=0\]