Question

Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form.
4, -14, and 5 + 8i

Answer 1

It is obvious that (x-4)(x-14) is two of the factors of the polynomial. Also, complex roots of a real polynomial must come in conjugate pairs, i.e. if a+bi is a root of a *real* polynomial, then a-bi will also be a root of the real polynomial.