If \( a x^{2}+b x+c=0 \) where \( a \neq 0 \) is satisfied by \( \alpha, \beta, \alpha^{2} \) and \( \beta^{2} \), where \( \alpha \beta \neq 0 \). Let set \( S \) be the set of all
P
possible unordered pairs \( (\alpha, \beta) \).
The match the following lists:
\begin{tabular}{|c|c|c|c|c|c|c|c|}
\hline & Column I & \multicolumn{2}{|c|}{ Column II } & & & & \\
\hline (A) & \begin{tabular}{l}
The number of elements in \\
set \( \mathrm{S} \) is
\end{tabular} & \( (\mathrm{P}) \) & 2 & & & & \\
\hline (B) & \begin{tabular}{l}
The sum of all possible \\
values of \( (\alpha+\beta) \) of the pair \\
\( (\alpha, \beta) \) in set \( S \) is
\end{tabular} & (Q) & 3 & & & & \\
\hline (C) & \begin{tabular}{l}
The sum of all possible \\
values of \( \alpha \beta \) of the pair \( (\alpha \), \\
\( \beta) \) in set \( S \) is
\end{tabular} & \( (\mathrm{R}) \) & 4 & & & & \\
\hline (D) & \begin{tabular}{l}
The sum of all possible \\
values of \( \alpha^{2}+\beta^{2} \) of the pair \\
\( (\alpha, \beta) \) in set \( S \) is, where \( \alpha \), \\
\( \beta \in R \) is
\end{tabular} & (S) & 1 & \begin{tabular}{l}
\( (1) \) \\
\( (2) \) \\
\( (3) \) \\
\( (4) \)
\end{tabular} & \begin{tabular}{l}
\( Q \) \\
\( R \) \\
\( Q \) \\
\( R \)
\end{tabular} & \begin{tabular}{l}
S \\
S \\
S \\
S
\end{tabular} & P \\
\hline
\end{tabular}
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