Let $p(x)$ and $q(x)$ are two monic polynomials with non negative roots such that $p(x)=f(x)-g(x)$ and $q(x)=f(x)-h(x)$. If we know all the roots of $f,g,h$, can we say anything about largest positive and smallest positive root of $p$ and $q?$
I have totally no idea how to think over it. Any help is highly appreciated.