- #1
utkarshakash
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Homework Statement
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
Homework Equations
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)'?