Nonzero redshift-drift root in flat matter-Lambda cosmology ($1+z_{\ast }=[{\Omega }_{\Lambda }+\sqrt{{\Omega }_{\Lambda }^2+4{\Omega }_m{\Omega }_{\Lambda }}]/(2{\Omega }_m)$)

For positive matter and vacuum fractions with ${\Omega }_m+{\Omega }_{\Lambda }=1$, redshift drift vanishes when $s^2={\Omega }_m{s}^3+{\Omega }_{\Lambda }$, $s=1+z$. Factoring out the trivial observer root $s=1$ leaves ${\Omega }_m{s}^2-{\Omega }_{\Lambda }s-{\Omega }_{\Lambda }=0$, giving the displayed positive root of a polynomial. It lies at a positive redshift exactly when ${\Omega }_m<2/3$. It is independent of the Hubble constant at fixed density fractions and is not the redshift of the acceleration-to-deceleration transition.