The condition for one root of ax3+bx2+cx+d=0 is sum of the other two roots, is

The given equation is ax3+bx2+cx+d=0 Let α,β,γ are the roots of given equationBy the given condition, one root is sum of other two rootsi.e., α =β+γ ∴s1=α+β+γ ⇒2α=−ba ⇒α=−b2a ∴  α  is one roots of the given equation∴   f(−b2a)=0 ⇒  a(−b2a)3+b(−b2a)2+c(−b2a)+d=0 ⇒  −b38a2+b34a2−bc2a+d=0 ⇒8a2d−4abc+b3=0