Equation, anyone?

Algebra Level 4

Which of the following statement is true about the equation $x\left| x \right| +a+bx=0$ , where $a$ , $b$ and $x$ are real.

(P) It has at most three roots

(Q) It has at least one real root

(R) Both (P) & (Q)

(S) It has real roots only if ${ b }^{ 2 }-4a\ge 0$

(T) None of these