Let $a,b\in\mathbb{R}$ be some fixed parameters. Show that the multistep methods described by $\rho(z)=(z-1)(\alpha{z}+1-\alpha)$, $\sigma(z)=(z-1)^2b+(z-1)a+\frac{(z+1)}{2}$ are of order $2$，and show that they are zero-stable if and only if $\alpha\ge\frac{1}{2}$.
Please help me with this question. It really confuses me.
I have computed out the method. It is $ay_{n+2}+(1-2a)y_{n+1}+(a-1)y_n=h(bf(x_{n+2},y_{n+2})+(a-2b+\frac{1}{2})f(x_{n+1},y_{n+1})+(a-1)f(x_n,y_n))$