Question Number 104775 by MAB last updated on 23/Jul/20

let P_n  an n-polynomial.  let a_1 ,...,a_n  its simple roots   let m_k  the slope of the tangent to P_n  at  the point (a_k ,0)  prove that  Σ_(k=1) ^n (1/m_k )=0  what about multiple roots?