If \( f(x)=\left|\begin{array}{ccc}0 & x-a & x-b \\ x+a & 0 & x-c \...

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If \( f(x)=\left|\begin{array}{ccc}0 & x-a & x-b \\ x+a & 0 & x-c \\ x+b & x+c & 0\end{array}\right| \), then
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(A) \( \quad f(a)=0 \)
(B) \( \quad f(b)=0 \)
(C) \( \dot{f}(0)=0 \)
(D) \( f(1)=0 \)
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