A settlement provided for in section 43-1404 means a voluntary agreement between the father of the child and the mother or some person authorized to act in her behalf, or between the father and the next friend or guardian of the child, whereby the father promises to make adequate provision for the support of the child. In the event that such a settlement is made it shall be binding on all parties and shall bar all other remedies of the mother and child and the legal representatives of the child so long as it shall be performed by the father, if said settlement is approved by the court having jurisdiction to compel the support of the child. The court shall approve such settlement only if it shall find and determine that adequate provision is made for the support of the child and that the father shall have offered clear evidence of his willingness and ability to perform the agreement. The court, in its discretion, may require the father to furnish bond with proper sureties conditioned upon the performance of the settlement.