Suppose that R(x) is a polynomial of degree 12 whose coefficients are real numbers. Also, suppose that R(x) has the following zeros. 3,-5i,5+i

Question

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

Other zeros are 5i, and 5 - i. Complex roots are always in conjugate pairs

With the 0 that is 5 of the 12 zeros. The other 7 must be 0.