Mathematics · Application of Derivatives

Let f : R → R be a twice differentiable function such that the quadratic equation f(x)m2 - 2f'(x)m + f''(x) = 0 in m, has two equal roots for every x &in startups; R. If f(0) = 1, f'(0) = 2 and (α, β) is the largest interval in which the function f(logex - x) is increasing, then α + β is equal to: