Hi,this one was quite difficult for me and just cant' get a good solution!

Determine the maximum value of \lambda such that if :
 f(x) = x^3 +ax^3 +bx+c is a cubic polynomial with all its roots nonnegative,then
 f(x) \geq \lambda{(x-a)}^3 ,
for all  x\geq0 . Also find the equality condition.

Thanks ahead,Adri