Question

suppose that r(x) is a polynomial of degree 9 whose coefficients are real numbers. also, suppose that R(x) has the following zeros. Answer the following.

Answer 1

The polynomial R(x) has degree 9. Two of the roots are 2i and -4-i.

(a) As the non-real roots lies along with its conjugates, the other roots of R(x) will be,

-2i and -4+i.

(b) The maximum number of real zeroes R(x) can have is 5, as there are 4 non-real roots that already exists.

(c).The maximum number of non real zeroes R(x) can have is 4.