What is the meaning of "v'Lamah Chashavtah ka'Zos Al Am Elokim"?
Rashi: Why did you suspect Yisrael, that [my family] would come to kill another without witnesses and warning? 1
Radak: Why did you think that they will not believe that you swore that my son will not die? 2
Malbim: How could you think that my story is true, that Bnei Yisrael would do (want to kill their relative) against what is natural and straight?
Why should he not be concerned lest her words are true? Surely David meant that he will send men to investigate, and if her story is true, they will do like David said! Perhaps she asks how he could swear in the name of Hashem before investigating; this implies that he was sure that it was true! (PF)
What is the source that David thought that people will not believe that he swore? She said this right after he swore! One could explain, why did you need to swear, for you thought that people will not believe what you say without a Shevu'ah? However, Radak's final words are unlike this, and he himself explained that she asked him to swear! (PF)
What is the meaning of "umi'Daber ha'Melech ha'Davar ha'Zeh k'Asham"?
Rashi: What you ruled for others, that they may not kill my son, now that I reveal to you that it applies to your two sons, do not regret and say 'I said this like Asham (Metzudas Tziyon - a mistake), and I retract', and the king will not return his son Avshalom who has been cast off. "Umi'Daber" means 'do not say.'
Radak: [Why did you think that that they will not believe that you swore 1 that my son will not die, rather, they will say that if] the king said so, it was b'Asham and mistakenly? For he does not return his son Avshalom who fled because he killed his brother Amnon. How can he swear that this one who killed his brother will not die or be cast off?!
Malbim: Midaber is like 'Misdaber' (like Rashi Bamidbar 7:89 says about "va'Yishma Es ha'Kol Midaber Elav"). What the king decided, he speaks about himself! This is like Asham (guilt), that he does not return his son.
Refer to 14:13:1:2*.