The sum of the real roots of the equation $$|x-2|^2+|x-2|-2=0$$ is

If the difference between the roots of $$x^2+a x+b=0$$ and that of the roots of $$x^2+b x+a=0$$ is same and $$a \neq b$$, then

For what values of $$a \in Z$$, the quadratic expression $$(x+a)(x+1991)+1$$ can be factorised as $$(x+b)(x+c)$$, where $$b, c \in Z$$ ?

If $$\frac{13 x+43}{2 x^2+17 x+30}=\frac{A}{2 x+5}+\frac{B}{x+6}$$, then $$A^2+B^2=$$