The determinant \( \Delta=\left|\begin{array}{ccc}a & b & a x+b \\ b & c & b x+c \\ a x+b & b x+...
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0The determinant \( \Delta=\left|\begin{array}{ccc}a & b & a x+b \\ b & c & b x+c \\ a x+b & b x+c & 0\end{array}\right| \) is equal to zero, if
(A) \( a, b, c \), are in A.P.
(B) \( a, b, c \), are in H.P.
(C) \( a, b, c \), are in G.P.
(D) \( x \) is a root of \( a x^{2}+b x+c=0 \)
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