how do you write a polynomial function of least degree that has rational coefficients, a leading coefficient of 1, and the zeros: x= 3, -2, -1+i

Answer 1

The complex conjugate of a complex zero must also be a zero, so you will have 4 zeros:

3

-2

-1 + i

-1 - i

f(x) = A (x - 3) (x + 2) [x - (-1 + i)] [ x - (-1 - i)]

The leading coefficient is A, which is given as 1, so

f(x) = (x - 3) (x + 2) [x - (-1 + i)] [ x - (-1 - i)]

If you expand this to standard form, all of the coefficients will come out real and rational.