Find an nth degree polynomial with real coefficients satisfying the given conditions

Question

n=3; -2 and -2+3i are zeros; leading coefficient is 1.

Answer 1

The complex conjugate of a complex zero must also be a zero, so the 3 zeros are

-2

-2 + 3i

-2 - 3i

With a leading coefficient of 1, the polynomial is

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

You can expand this to standard form if you wish. All the coefficients will come out real when you simplify.