(a) (b) Prove that log, 5 is irrational Suppose that a and b are real numbers where b# 0 Consider the polynomial P(z)=z + az + b The polynomial has a double root at z = a (i) Show that P'(z) is an odd function. Show that - a is also a double root a E (iii) (iv) ((v)) Prove that b = For what value(s) of a does P(z) have double root equal to 3i For what values of a does P(z) have Real roots?