If \[\alpha ,\beta \] are the roots of \[a{{x}^{2}}+bx+c=0\] and \[\alpha +\beta ,\] \[\,{{\alpha }^{2}}+{{\beta }^{2}},\] \[\,{{\alpha }^{3}}+{{\beta }^{3}}\] are in G.P., where \[\Delta ={{b}^{2}}-4ac\], then [IIT Screening 2005]

If \[\alpha ,\beta \] are the roots of \[a{{x}^{2}}+bx+c=0\] and \[\al

1.	If \[\alpha ,\beta \] are the roots of \[a{{x}^{2}}+bx+c=0\] and \[\alpha +\beta ,\] \[\,{{\alpha }^{2}}+{{\beta }^{2}},\] \[\,{{\alpha }^{3}}+{{\beta }^{3}}\] are in G.P., where \[\Delta ={{b}^{2}}-4ac\], then [IIT Screening 2005]
A.	\[\Delta \ne 0\]
B.	\[b\Delta =0\]
C.	\[cb\ne 0\]
D.	\[c\Delta =0\]
Answer» E.

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If \[\alpha ,\beta \] are the roots of \[a{{x}^{2}}+bx+c=0\] and \[\alpha +\beta ,\] \[\,{{\alpha }^{2}}+{{\beta }^{2}},\] \[\,{{\alpha }^{3}}+{{\beta }^{3}}\] are in G.P., where \[\Delta ={{b}^{2}}-4ac\], then [IIT Screening 2005]

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