Let \( \Delta=\left|\begin{array}{ccc}-b c & b^{2}+b c & c^{2}+b c \\ a^{2}+a c & -a c & c^{2}+a...

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Let \( \Delta=\left|\begin{array}{ccc}-b c & b^{2}+b c & c^{2}+b c \\ a^{2}+a c & -a c & c^{2}+a c \\ a^{2}+a b & b^{2}+a b & -a b\end{array}\right| \) and the equation \( p x^{3}+q x^{2}+r x+s=0 \) has roots \( a, b, c \), where \( a, b, c \in R^{+} \). The value of \( \Delta \) is
(a) \( r^{2} / p^{2} \)
(b) \( r^{3} / p^{3} \)
(c) \( -S / p \)
(d) None of these
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