Find the roots of each of the following equations, if they exist, by applying the quadratic formula:
$=x^2-(\sqrt{3}+1)x+\sqrt{3}=0$

Find the roots of each of the following equations, if they exist, by applying the quadratic formula:

$\frac{1}{x}-\frac{1}{x-2}=3, x\ne 0, 2$

If $\alpha$ and $\beta$ are the roots of the equation, then find  $\sqrt{3}\left|\alpha -\beta \right|$