3. Given the three sides of $\triangle A B C$ are $a, b, c$, and they satisfy the equation $a^{2} x^{2}-\left(c^{2}-a^{2}-b^{2}\right) x+b^{2}=0$. Then the nature of the roots of the equation is ( ).
(A) has two equal real roots
(B) has two distinct real roots
(C) has no real roots
(D) cannot be determined
3.C.
$$
\begin{array}{l}
\Delta=\left(c^{2}-a^{2}-b^{2}\right)^{2}-4 a^{2} b^{2} \\
=(c+a-b)(c-a+b)(c+a+b)(c-a-b) .
\end{array}
$$

Since $c+a-b>0, c-a+b>0$,
$$
c+a+b>0, c-a-b<0 \text {, }
$$

Therefore, $\Delta<0$, the original equation has no real roots.