# Arithmetic Progresion + Quadratic Equation = Nice Problem

Algebra Level pending

Given that $$c$$, $$b$$ and $$a$$ are consecutive terms in a arithmetic progression. If the equation $$ax^2+bx+c=0$$ has $$c$$ as solution and $$a,b,c \ne 0$$. The value of the common difference can be written as $$\frac{\sqrt{\alpha}}{\beta}$$. Find the value of $$\alpha+\beta$$

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