Reduced to one healthy quarterback, the 49ers on Tuesday signed veteran free agent Jesse Palmer, who played four seasons for the New York Giants before he was released this summer. Contract details were not yet available, but it is likely that Palmer signed a one-year deal for the minimum base salary of $540,000, prorated over the balance of this season. Team sources said that Palmer would likely spend three or four weeks on the roster, or until the injured quarterbacks are recovered. Rookie Alex Smith, the top overall selection in the 2005 draft, is battling a sprained right knee. Backup Ken Dorsey, who started last week's game, has a left ankle injury and is in a walking boot. San Francisco may be forced to start Cody Pickett, who finished up last Sunday's victory over Tampa Bay, in this weekend's game against the New York Giants. He would be the fourth different starter employed by San Francisco this season.