Father is B+, Mother is A+, and Child is O+. What are the genotypes of the parents?

Child is O blood type, so genotype must be $ii$. This means both parents must carry the 'i' allele.Father (B type) must be $I^{B}i$.Mother (A type) must be $I^{A}i$.If either was homozygous ($I^B{I}^B$ or $I^A{I}^A$), the child could not be O type.