Consider we have a stricktly increasing positive sequence $\lambda_n$ and the following sixth order algebraic equation for every $n\in \mathbb{N}$, $$\zeta s^6-s^4+\lambda_n^2=0,$$
where $\zeta$ is a positive constant. I am wondering whether all of the six roots of this algebraic equation are monotone or not (in case of having an imaginary root we look at the absolute value)? How can we pass the monotonicity of a parameter, like $\lambda_n$, in the equation to the roots of that equation?