If one root of x3−12x2+kx−18=0 is thrice the sum of remaining two roots then k =

The given equation is f(x)=x3−12x2+kx−18=0 Let α,β,γ  are the rootsGiven that, one root is thrice the sum of remaining two roots⇒α=3(β+γ) ∴  sum of the roots : α+β+γ=12 ⇒α+α3=12 ⇒4α=36⇒α=9 f(9)=0 ⇒(9)3−12(9)2+k(9)−18=0 ⇒k=29