The solution of the differential equation \[ \frac{d^3 y}{dx^3}-5.5\,\frac{d^2 y}{dx^2}+9.5\,\frac{dy}{dx}-5\,y=0 \] is expressed as $y=C_1 e^{2.5x}+C_2 e^{\alpha x}+C_3 e^{\beta x}$, where $C_1,C_2,C_3,\alpha,\beta$ are constants, with $\alpha$ and $\beta$ distinct and not equal to $2.5$. Which of the following options is correct for the values of $\alpha$ and $\beta$?