## Find the maximum values of a real constant

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.