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

Determine the maximum value of $\displaystyle \lambda$ such that if :

$\displaystyle f(x) = x^3 +ax^3 +bx+c $ is a cubic polynomial with all its roots nonnegative,then

$\displaystyle f(x) \geq \lambda{(x-a)}^3$ ,

for all $\displaystyle x\geq0$ . Also find the equality condition.

Thanks ahead,Adri