The solution of the differential equation

\(\rm \frac{d^3y}{dx^3}-5.5\frac{d^2y}{dx^2}+9.5\frac{dy}{dx}-5y=0\)

is expressed as 𝑦 = 𝐶₁𝑒^2.5𝑥 + 𝐶₂𝑒^𝛼𝑥 + 𝐶₃𝑒^𝛽𝑥 , where 𝐶₁, 𝐶₂, 𝐶₃, 𝛼, and 𝛽 are constants, with α and β being distinct and not equal to 2.5. Which of the following options is correct for the values of 𝛼 and 𝛽?