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Let \( f(x)=a x^{2}+b x+c \). If \( x_{1}, x_{2}, x_{3} \) are three distinct real numbers such that \( f\left(x_{1}\right)=f\left(x_{2}\right)=f\left(x_{3}\right)=0 \), then \( f(x) \equiv 0 \), i.e. \( f(x)=0 \forall x \in \mathbf{R} \).
If \( f \) and \( x_{1}, x_{2}, x_{3} \) are as in the above paragraph, then
(a) \( a \neq 0, b \neq 0, c=0 \)
(b) \( a=b \neq 0, c=0 \)
(c) \( a=b=c=0 \)
(d) \( a \neq 0, b=c=0 \).
E
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