Multiplier relation for three distinct fixed points of a quadratic rational map
= Multiplier relation for three distinct fixed points of a quadratic rational map
If a quadratic rational map has three distinct fixed points with multipliers $\lambda_0,\lambda_1,\lambda_2$, then $\lambda_i\lambda_j\ne1$ for $i\ne j$. Otherwise the two corresponding indices already sum to one, contradicting the nonzero third index.