BG-MO 1963 Problem 2

It is given the equation $x^2+px+1=0$ , with roots $x_1$ and $x_2$ ;

(a) find a second-degree equation with roots $y_1,y_2$ satisfying the conditions $y_1=x_1(1-x_1)$ , $y_2=x_2(1-x_2)$ ; (b) find all possible values of the real parameter $p$ such that the roots of the new equation lies between $-2$ and $1$ .