Final answer:
The polynomial function with a leading coefficient of one and given roots can be found using the complex conjugate theorem.
Step-by-step explanation:
The polynomial function with a leading coefficient of one and roots (7 + i) and (5 - i) with multiplicity one can be determined by using the complex conjugate theorem. The theorem states that if a complex number is a root of a polynomial with real coefficients, then its conjugate is also a root. Therefore, the roots of the polynomial will be (7 + i), (7 - i), (5 - i), and (5 + i). The polynomial can be expressed as (x - (7 + i))(x - (7 - i))(x - (5 - i))(x - (5 + i)). Multiplying these factors together results in the polynomial function (x - 7 - i)(x - 7 + i)(x - 5 + i)(x - 5 - i). Therefore, the correct option is option B. (x - 7 + i)(x - 5 - i).