The sum of all the roots of the equation $(x-1)^2-5|x-1|+6=0$, is :

The sum of the squares of the roots of $ |x-2|^2 + |x-2| - 2 = 0 $ and the squares of the roots of $ x^2 - 2|x-3| - 5 = 0 $, is

The number of real roots of the equation $x |x - 2| + 3|x - 3| + 1 = 0$ is :

Let the set of all values of $p \in \mathbb{R}$, for which both the roots of the equation $x^2-(p+2) x+(2 p+9)=0$ are negative real numbers, be the interval $(\alpha, \beta]$. Then $\beta-2 \alpha$ is equal to