Find the nth degree polynomial function with real coefficients satisfying the given conditions. n=3; - 2 and 2+3i are zeros; leading coefficient is 1.

f (x) = x^3 - 2x^2 + 5x + 26

Step-by-step explanation:

When p is a root, (x - p) is a factor.

If the polynomial has real coefficients, its complex roots come in conjugate pairs. Then the linear factorization for the given roots is ...

f (x) = (x + 2) (x - 2-3i) (x - 2+3i) = (x + 2) (x^2 - 4x + 13)

f (x) = x^3 - 2x^2 + 5x + 26