The polynomial $x^3+x-3=0$ has roots $\alpha$, $\beta$ and $\gamma$. If $\frac{a\alpha+1}{\alpha-b}$, $\frac{a\beta+1}{\beta-b}$ and $\frac{a\gamma+1}{\gamma-b}$ are the roots of another cubic, what are the conditions on $a$ and $b$ given that the two cubics are the same?
Where should I start this? Using Vieta's formulas, this is tedious and I got stuck with too many unknowns. Please help