What is the only genotype of two parents that would ensure that their offspring could not roll their tongue

tt genotype of both parents

Explanation:

Since tongue rolling is genetically dominant trait, this means that even a single copy of the dominant gene (for tongue rolling) is enough for the kids to express the trait. The dominant allele for the gene is indicated by capital T and the recessive allele for non-rolling tongue is indicated by small t.

Since the trait of rolling tongue is dominant in nature, it means that even if one of the parents is heterozygous or homozygoud for T (TT), there will be chances that kids will be tongue rollers. So the only case when any of the kids will never be tongue rollers is one when both parents are homozygous for the allele (tt) that is for non-tongue rolling. Attached genetic picture will help you understand better.

Hope it helps

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