10. a. T or \( \mathrm{F}: \) A 3rd degree polynomial can have 3 non-real roots. b. T or \( \mathrm{F}: \mathrm{f}(\text{x})=(\text{x}-3)^{3}(\text{x}-6) \) has a zero with multiplicity 3.

A 3rd degree polynomial can have a maximum of three roots, and the roots can be a mix of real and complex numbers. By the fundamental theorem of algebra, it can have either all real roots or one real root with a pair of complex conjugates. Thus, the statement is false; a 3rd degree polynomial cannot have 3 non-real roots. The function \(f(x)=(x-3)^{3}(x-6)\) has a zero at \(x=3\) with a multiplicity of 3, because \((x-3)\) appears three times in its factorization. Additionally, it has another zero at \(x=6\) with multiplicity 1. Therefore, the statement is true, confirming the nature of the roots.