Answer: PP and Pp.
Explanation: Based on the information provided, the genotypes of the purple-flowered parents could be either homozygous dominant (PP) or heterozygous (Pp).
If both parents are homozygous dominant (PP), all of their offspring would be expected to have purple flowers, since each parent would contribute a dominant P allele.
If both parents are heterozygous (Pp), then they would each contribute one dominant P allele and one recessive p allele to their offspring. The offspring would have a 25% chance of inheriting two recessive alleles (pp) and thus having white flowers.
Therefore, there are two possibilities for the genotypes of the parents: PP and Pp.