In pea plants, smooth seed texture is dominant over wrinkled seed texture. A gardener has a pea plant that produces smooth seeds. How can the Gardener determine whether the plant is homozygous?

By test crossing the pea plant with a homozygous recessive pea plant

Explanation:

A test cross involves crossing of an individual with doubtful genotype with an individual that is homozygous recessive for the same trait in order to determine whether the individual with doubtful genotype is homozygous or heterozygous for the trait in question.

Assuming the gardener's pea plant is homozygous (SS), one would expect all the progeny to be smooth seeded when the pea plant is test-crossed with a homozygous recessive pea plant such that

SS x ss = Ss, Ss, Ss and Ss (assuming the allele for seed texture to be S)

Assuming the gardener's pea plant is heterozygous (Ss):

Ss x ss = Ss, Ss, ss and ss. Hence, one would expect 50% of the progeny to be smooth seeded and 50% to be wrinkled seeded.