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 $f(-r_1),~f(-r_2),~f(-r_3)$.
You can help us out by revising, improving and updating this answer.Update this answer
After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.