A quadratic equation $ax^2+bx+c=0$ has equal roots at $a=2c$. How could we find the sum of reciprocals of the roots of this equation? 
A quadratic equation $ax^2+bx+c=0$ has equal roots at $a=2c$. How
  could we find the sum of reciprocals of the roots of this equation?

I need some hints for solving this problem.

Also, just for the fun of it, since you have a root with multiplicity two:
$$
ax^2+bx+c = (\sqrt{a}x+\sqrt{c})^2
$$
Then the root is $x^* = \pm\sqrt{\frac{c}{a}}$ and from $a = 2c$, we get $x^* = \pm\sqrt{\frac{1}{2}}$. Hence, $$
\frac{1}{x_1}+\frac{1}{x_2} = \frac{2}{x^*}=\pm 2{\sqrt{2}}$$
