Which is the polynomial function of lowest degree with rational real coefficients, a leading coefficient of 3 and roots square root of 5 and 2 ?

Because the polynomial has rational coefficients and √5 is a root, its conjugate −√5 must also be a root. Together with the root 2, the lowest-degree polynomial is 3(x − √5)(x + √5)(x − 2), where 3 gives the required leading coefficient. Expanding gives 3(x² − 5)(x − 2) = 3x³ − 6x² − 15x + 30, which is choice C.

AI-written and checked against the verified answer.