Numerical Methods: Euler to Runge–Kutta · Challenge problem

The leapfrog (explicit midpoint) two-step method $y_{n+1} = y_{n-1} + 2h\,f(t_n, y_n)$ is applied to $y' = -y$ with $h = \dfrac{3}{4}$. Its iterates have the form $y_n = A\xi_1^{\,n} + B\xi_2^{\,n}$, where $\xi_1, \xi_2$ are the roots of the characteristic equation. What is the larger of $|\xi_1|$ and $|\xi_2|$?