Where do we derive (the need for) bedikoth (general examination of the facts, of lesser magnitude than chakiroth)? From (Ibid. 13:15) "and, behold, true and correct is the thing."
If in the end we include bedikoth, why chakiroth? With chakiroth, if one of them (the witnesses) said "I do not know," their testimony is invalidated. With bedikoth, if one of them, or even both of them said "I do not know," their testimony stands.
Both with chakiroth and bedikoth, if they refute each other, their testimony is invalidated.