7. a. (2 pts) Give an example of a polynomial P(z) with all real coeflicients, and four different non-real roots, one of which is 2i. b. (1 pt) Give an example of a polynomial P(z) with all real coeflicients, where 2i is a repeated root. c. (3 pts) Suppose that r is a double root of a polynomial P(z). Show that r is a root of the derivative P'(z). d. (1 pt) Give an example of a non-constant polynomial in z and the conju- gate variable Z so that P(z, Z) is positive (never zero) for all z in C. e. (2 pts) Let n = 2 be a positive integer. Factor the degree n polynomial z 1 as a linear polynomial times a degree n 1 polynomial. (Hint: there is a real number that is a root for any n)