Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form.

8, -14, and 3 + 9i

Question

Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form.

8, -14, and 3 + 9i

anonymous · Answer

note that if a polynomial has real coefficients with a complex zero $z=a+bi$ then it is necessary that $\bar{z}=a-bi$ is also a complex zero... $P(a+bi)=P(a-bi)=0$ http://en.wikipedia.org/wiki/Complex_conjugate_root_theorem

anonymous · Answer

so if $3+9i$ is a root then so is $3-9i$ necessarily giving us:$$P(x)=(x-8)(x+14)(x-(3+9i))(x-(3-9i))$$can you distribute that out?