2. If $f(x)=a x^{2}+b x(a, b$ are non-zero real constants) has two distinct imaginary roots $x_{1}, x_{2}$, such that $f\left(x_{1}\right)=$ $f\left(x_{2}\right)=c \in R$, then the relationship between $b^{2}+4 a c$ and zero is ( ).
(A) $b^{2}+4 a c>0$
(B) $b^{2}+4 a c=0$
(C) $b^{2}+4 a c<0$
(D) Cannot be determined.
2. C

From the given, $x_{1}, x_{2}$ are the two imaginary roots of the quadratic equation with real coefficients
$$
a x^{2}+b x-c=0
$$

with the discriminant being less than 0, i.e., $b^{2}+4 a c$ $<0$