Trustees at Polytechnic University in Brooklyn have approved a merger with New York University, despite an ongoing investigation by a state senator and questions from the attorney general’s office. Polytechnic postponed its merger vote last month after Sen. Kenneth LaValle, the Republican chairman of the Senate’s Higher Education Committee, said he was investigating ethical and legal concerns. Opponents say NYU was only interested in acquiring Polytechnic’s real estate. “We’re giving N.Y.U. millions and millions of dollars in real estate, with little in return, other than the ability to use their name,” said George Likourezos, president of the Polytechnic alumni association. “It’s a lopsided deal.” Polytechnic has a 650,000-square-foot campus in Brooklyn’s MetroTech Center and holds air rights that developer Forest City Ratner could be interested in buying.