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

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