1. The problem statement, all variables and given/known data Let f:R→R be a continuous and differentiable function, then prove that the equation f'(x)+λf(x)=0 has at least one real root between any pair of roots of f(x)=0, λ being a real number 2. Relevant equations 3. The attempt at a solution All that I know from Rolle's Theorem is that between a pair of roots of f(x) there must be atleast one root of f'(x). But I can't figure out how to deal with that extra term 'λf(x)'?