Observation of the rare decay B^{+}→K^{+}π^{0}π^{0} and measurement of the quasi-two-body contributions B^{+}→K*(892)^{+}π^{0}, B^{+}→f_{0}(980)K^{+}, and B^{+}→χ_{c0}K^{+}

We report an analysis of the charmless hadronic decays of charged B meson to the final state K+pi0pi0, using a data sample of 470+/-2.8 million BBbar events collected at the Y(4S) resonance. We observe an excess of signal events, with a significance above 10 standard deviations including systematic uncertainties, and measure the branching fraction and CP asymmetry to be B(B+->K+pi0pi0)=(16.2+/-1.2+/-1.5)x10^-6 and A_CP(B+->K+pi0pi0)=-0.06+/-0.06+/-0.04, where the uncertainties are statistical and systematic respectively. Additionally we study the contributions of the B+->K*(892)+pi0, B+->f0(980)K+ and B+->chic0K+ quasi-two body decays. We report the world's best measurements of the branching fractions and CP asymmetry of the B+->K+pi0pi0 and B+->K*(892)+pi0 channels.