I have a cubic equation of the form $$x^3-a^2x-b^2=0.$$
It is given that all roots are real, moreover, only one root is positive and the other two are negative. Let the positive root be $\alpha>0$. Can I express $\alpha$ in terms of $a,b$? In the problem $a,b$ are some function of $t$ and I have to differentiate $\alpha$ w.r.t. $t$.