Question #3-6 Marks If P(x) is a polynomial and c is a constant for which P(e)-0, then c is called a zero of P(). If P(z)-(x-c)mQ(x) where Q(c)0, then c is a zero of P(z) with multiplicity equal to m. It is well known that zeros of polynomials with large multiplicity are ill-conditioned This question is an example that illustrates th (e) (2 points) Clearly P(x) (-1.5)- +13.52 -13.5z + 5.0625 has a zero of multiplicity m- 4 at c -1.5. Now, consider the polynomial R() +13.5x +13.5r +5.06249999 (r 1.5)-10- which is obtained by perturbing the constant coefficient of P(x) by 10-5. Compute exactly (using algebra) the four zeros of R() Note: This can be most easily done by noting that R(r)-0 imples that (r-15) 10-. This polynomial equation has 2 real roots and 2 complex conjugate roots. De- termine them exactly (b) (4 points) Conclude that the problem of computing the zeros of P(r) is ill-conditioned. Do this as follows. Determine the relative change in the magnitude of the constant t when Pr) is perturbed to R(r), and compare this with the relative change in the magnitude of one of the zeros of P(r). Use the largest real root of R(r) for this computation