Writing a function from given zeros

Question

Write a polynomial function  of least degree that has rational coefficients, a leading coefficient of 1 and the zeros 4, 3, and -i

Answer 1

Given the zeros, we know that the function should have the following expressions: (x-4), (x-3), and (x²+1). So the function is:

f(x) = (x-4)(x-3)(x²+1)

You can multiply it out if you need it in standard form.