Let  $P\left(x\right)=x^2+bx+c(b,c\in R)$,then which of the following statements implies that $P\left(P\left(x\right)\right)=0$has atleast one negative root.

a) P(x) = 0 has roots of opposite signs
 
$P\left(P\left(x\right)\right)=0\Rightarrow P\left(x\right)=\alpha$ or $\beta$  ; let  $\alpha >O\&\beta <0$
$\Rightarrow P\left(x\right)=\alpha$ has atleast one negative roots
 
d)$P\left(\frac{4C-b^2}{4}\right)<0\Rightarrow P\left(x\right)$  should have real roots
$\Rightarrow b^2-4C>0$ 
$\Rightarrow 4C-b^2<0$ ; 
$b>0$                      $\Rightarrow$sum of roots is -ve