Final answer:
To find the nth degree polynomial function with n = 3 and zeros 3 and I, we can use the fact that the zeros of the polynomial are the values of x where the function equals zero. By substituting the zeros into the polynomial and using the given information, we can solve for the unknown coefficients.
Step-by-step explanation:
To find the nth degree polynomial function with n = 3 and zeros 3 and I, we know that the zeros of the polynomial are the values of x where the function equals zero. So, if 3 and I are zeros of the polynomial, we can write the polynomial as (x - 3)(x - I)(x - I). To find the specific coefficients, we can use the given information that f(2) = 25. We can substitute x = 2 into the polynomial and solve for the coefficient. In this case, we get (2 - 3)(2 - I)(2 - I) = -1 * (2 - I)(2 - I). Since we know f(2) = 25, we can set the polynomial equal to 25 and solve for the unknown coefficient.