Section 14. Upon a petition of an executor or administrator for a license to sell real estate of the deceased or of a guardian or conservator to sell real estate of his ward, the court may, if the petitioner so requests, authorize him to sell such property at public auction and to convey to the purchaser all the estate, right, title and interest which the deceased had therein at his death and which was then chargeable with the payment of his debts or which the ward has at the time of the sale. If the petitioner requests that such property may be sold by private sale and the court, upon a hearing, finds that an advantageous offer for the purchase thereof has been made to the petitioner, and that the interests of all parties will be promoted by an acceptance thereof, it may authorize a conveyance by private sale in accordance with such offer or upon other terms; but the petitioner so authorized may nevertheless sell such property by public auction in accordance with this chapter. The court, if satisfied that such action will not be prejudicial to the interests of the estate, may authorize the petitioner to become the purchaser of such real estate at public or private sale.