Let \( f(x)=a x^{2}+b x+c \). If \( x_{1}, x_{2}, x_{3} \) are thre...
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 \( f(x) \equiv 0 \),
If \( g(x)=x_{1} \frac{\left(x-x_{2}\right)\left(x-x_{3}\right)}{\left(x_{1}-x_{2}\right)\left(x_{1}-x_{3}\right)} \)
\[
+x_{2} \frac{\left(x-x_{3}\right)\left(x-x_{1}\right)}{\left(x_{2}-x_{1}\right)\left(x_{2}-x_{3}\right)}+x_{3} \frac{\left(x-x_{1}\right)\left(x-x_{2}\right)}{\left(x_{3}-x_{1}\right)\left(x_{3}-x_{2}\right)}
\]
then \( g(x) \) is identically equal to
(a) 0
(b) 1
(c) \( x \)
(d) \( \left(x-x_{1}-x_{2}-x_{3}\right)^{2}+ \)
\( \left(x_{1}^{2}+x_{2}^{2}+x_{3}^{2}\right) x-x_{1} x_{2} x_{3} \)
P
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