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

Help please?

Answer 1

easy. so the polynomial function of minimum degree has to be at least 4. this is because you have at least four roots. you have 4, -14, 5 + 8i AND 5 - 8i. this is because of the complex root theorem, which says if a complex number a+bi is a root then its conjugate a-bi will also be a root. so the polynomial now looks like this:

(x-4)(x+14)(x-5-8i)(x-5+8i)

multiply these terms together and you have your polynomial

Answer 2

Thank you for your help! I got x^4 -67x^2 + 1,450x - 4,984