Question

Suppose that R(x) is a polynomial of degree 11 whose coefficients are real numbers. Also, suppose that R(x) has the following zeros. 5-4i, -4-5i, -3i Answer the following. (a) Find another zero of R(x). (b) What is the maximum number of real zeros that R(x) can have? (c) What is the maximum number of nonreal zeros that R(x) can have?

Answer 1

(a) Complex roots are always in conjugate pairs, so another zero of R(x) are -5-4i, 4-5i, 3i