We introduce a special class of real recurrent polynomials $f_m$$($m{geq}1$) of degree m+1, with positive roots $s_m$, which are decreasing as m increases. The first root $s_1$, as well as the last one denoted by $s_{infty}$ are expressed in closed form, and enclose all $s_m$ (m > 1). This technique is also used to find weaker than before [6] sufficient convergence conditions for some popular iterative processes converging to solutions of equations.