Upon a petition filed with the circuit court of any county to which the provisions of this article are applicable signed by a number of registered voters of the county equal to fifteen per centum of the number of votes cast in the county in the preceding presidential election asking that a referendum be held on the question of changing the method of selection of members of the county school board, the court shall, by order entered of record, require the regular election officials on the day fixed in such order to open the polls and take the sense of the qualified voters of the county on the question printed on the ballot as herein provided. The clerk of the county shall cause a notice of such referendum to be published in some newspaper published or having a general circulation in the county once a week for three successive weeks prior to such referendum and shall post a copy of such notice during the same time at the front door of the courthouse of the county. In lieu of such petition, the Board of Supervisors of Isle of Wight County or Roanoke County may cause to be passed a resolution requesting that such referendum be held; provided that prior to the passage of such resolution the Board of Supervisors shall hold a public hearing on the question of such referendum. The resolution shall be filed with the circuit court and upon receipt thereof, the court shall proceed as in the case of a petition. The ballots used in the referendum shall be printed as follows: “Shall the present method of selecting the members of the county school board be changed from appointment by the School Board Selection Commission to appointment by the governing body of the county? Yes [ ] No [ ]” The ballots shall be counted, returns made and canvassed as in other elections, and the results certified by the electoral board to the State Board of Elections, the clerk of the county and the circuit court; and the court shall enter of record the results of such referendum.