158 4. Equations
9.5. Note that the conditions imply that ct + d = a-‘c(at + b).9.6. Noting that the relation 1 + w + w 2 = 0 is a good way of disposing of
excess terms, calculate Ip( + jp(wz)j” + lp(w2r)j2, where w is an
imaginary cube root of unity.9.8. Write the derivative r(t) as a product of irreducible powers which di-
vide f(t) and a polynomial g(t). D oes g(t) have any zeros in common
with f(t)? What is the degree of g(t)?9.9, By way of reconnoitring, look first at the possibility that p(t) has only
simple zeros. What can be said of the zeros of (p - q)(t)? of p’(t)?