$\because 、\left(20\right.$ points) For a quadratic equation with real coefficients $a x^{2}+2 b x$ $+ c=0$ having two real roots $x_{1}, x_{2}$. Let $d=\left|x_{1}-x_{2}\right|$. Find the range of $d$ when $a>b>c$ and $a+b+c=0$.