Write a polynomial function f

Question

Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros. Write the polynomial in standard form.

3, 4+i

Answer 1

The complex conjugate of a complex zero must also be a zero, so you will have 3 zeros:

3

4 + i

4 - i

f(x) = (x - 3) [x - (4 + i)] [x - (4 - i)]

You expand this to standard form. The coefficients will all come out real.