Answer
It is not possiblie to determine the zeros of the function $g$.
Work Step by Step
We have that: $f(r_1)=f(r_2)=f(r_3)=0$
$g(r_1)=f(-r_1)$
$g(r_2)=f(-r_2)$
$g(r_3)=f(-r_3)$
But, we do not know the values of $f(-r_1),~f(-r_2),~f(-r_3)$.