Sentence:  The aim of this paper consists on the study of the following fourth-order operator: \begin{equation}\label{Ec::T4} T[M]\,u(t)\equiv u^{(4)}(t)+p_1(t)\,u"'(t)+p_2(t)\,u"(t)+M\,u(t)\,,\ t\in I \equiv [a,b]\,, \end{equation} coupled with the two point boundary conditions: \begin{equation}\label{Ec::cf} u(a)=u(b)=u"(a)=u"(b)=0\,. \end{equation} So, we define the following space: \begin{equation}\label{Ec::esp} X=\left\lbrace u\in C^4(I)\quad\mid\quad u(a)=u(b)=u"(a)=u"(b)=0 \right\rbrace \,. \end{equation} Here p_1\in C^3(I) and p_2\in C^2(I). By assuming that the second order linear differential equation \begin{equation}\label{Ec::2or} L_2\, u(t)\equiv u"(t)+p_1(t)\,u'(t)+p_2(t)\,u(t)=0\,,\quad t\in I, \end{equation} is <WSD>disconjugate</WSD> on I, we characterize the parameter's set where the Green's function related to operator T[M] in X is of constant sign on I \times I. 
Meaning of the word marked with <WSD> tags:  Having at most one fewer zeros (including multiplicities) than the dimension of the problem space.