write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the zeros 2i and -3 + (radical) 5

Answer 1

Imaginary and irrational zeros come in conjugate pairs,

So, the zeros are +2i, -2i, -3+(radical)5 and -3-(radical)5.

The first two zeros come from setting x^2+4=0 and the second two zeros come from setting x^2+6x+4=0.

Multiplying the trinomial by the binomial gives us the resultant degree 4 polynomial function of x^4+6x^3+4x^2+24x.