2. Let $a, b$ be the radii of two circles, and $c$ be the distance between their centers. If the equation $x^{2}-2 a x+b^{2}=c(b-a)$ has equal real roots, then the two circles ( ).
(A) intersect
(B) are internally tangent
(C) are equal
(D) are equal or externally tangent
2.(D).

According to the problem, we have $\Delta=0$, that is, $a^{2}-\left[b^{2}-c(b-a)\right]=0$. Factoring, we get $(a-b)(a+b-c)=0$. When $a-b=0$, the two circles are equal, and when $a+b-c=0$, the two circles are externally tangent.