CMO 2022 Problem 2

Find the largest real number $\lambda$ with the following property: for any positive real numbers $p,q,r,s$ there exists a complex number $z=a+bi$ ( $a,b\in \mathbb{R})$ such that $$|b|\ge \lambda |a| \text{and} (pz^3+2qz^2+2rz+s) \cdot (qz^3+2pz^2+2sz+r) =0.$$