The sum of the roots of $$\frac{1}{x+a}+\frac{1}{x+b}=\frac{1}{c}$$ is zero. The product of roots is

A

0

B

$$\frac{a+b}{2}$$

C

$$-\frac{1}{2}(a^2+b^2)$$

D

$$2(a+b)^2$$