Exercise 5.  Let    be a polynomial of degree n.

 5 (c).  Find an example of a polynomial that has some roots occuring as complex conjugates, and some not.
Hint.  Find a polynomial for part 5 (a), another for part 5 (b), and multiply them together.

Solution 5 (c).

See text and/or instructor's solution manual.

For part 5 (a), consider   .

For part 5 (b), consider   .

The polynomial  

      

has some roots occuring as complex conjugates, and some not.

This solution is complements of the authors.

(c) 2008 John H. Mathews, Russell W. Howell