If the equation $|x^2+bx+c|=k$ has four real roots ..... 
If the equation $|x^2+bx+c|=k$ has four real roots  then which of the following option is  correct :
(a) $b^2-4c >0$ and $0<k<\frac{4c-b^2}{4}$
(b) $b^2-4c <0$ and $0<k<\frac{4c-b^2}{4}$
(c) $b^2-4c >0$ and $0<k>\frac{4c-b^2}{4}$

Please suggest how to proceed in this problem , I am getting no clue on this.. please help thanks.

Hint: Clearly $k$ is positive. Also, both 
$$ x^2+bx + (c-k) = 0 $$
and $$ x^2+bx + (c+k) = 0 $$
have real roots (that is, both equation discriminants are positive).
(I have been assuming everywhere that there are four distinct real roots.)

 Note that $k>0$ and positivity of the second discriminant, $b^2-4(c+k)>0$ imply $b^2-4c>4k>0$, so $b^2-4c>0$. The third inequality comes directly from the positivity of the first discriminant, $b^2-4(c-k)>0$. 

