Results are presented from a search for the pair production of first- and second-generation scalar leptoquarks in proton-proton collisions at root s = 7 TeV. The data sample corresponds to an integrated luminosity of 5.0 fb(-1), collected by the CMS detector at the LHC. The search signatures involve either two charged leptons of the same flavor (electrons or muons) and at least two jets or a single charged lepton (electron or muon), missing transverse energy, and at least two jets. If the branching fraction of the leptoquark decay into a charged lepton and a quark is assumed to be beta = 1, leptoquark pair production is excluded at the 95% confidence level for masses below 830 GeV and 840 GeV for the first and second generations, respectively. For beta = 0.5, masses below 640 GeV and 650 GeV are excluded. These limits are the most stringent to date.