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Let f : R \to R be a twice differentiable function such that the quadratic equation f(x)m^2 - 2f(x)m + f'(x) = 0 in m, has two equal roots for every x \in R. If f(0) = 1, f'(0) = 2 and (α, β) is the largest interval in which the function f(\log_e x - x) is increasing, then α + β is equal to: | Watch the step-by-step video solution for this NIMCET PYQ.