8 Throughout this question the use of a calculator is not permitted. The polynomial z* + 322 + 6z + 10 is denoted by p(z). The complex number -1 + i is denoted by ut. (i) Showing all your working, verify that u is a root of the equation p(z) = 0. (13] (ii) Find the other three roots of the equation p(z) = 0. [7] 10 The diagram shows the curve y = (Inx). The x-coordinate of the point P is equal to e, and the normal to the curve at P meets the x-axis at Q. (i) Find the x-coordinate of Q. [4] (ii) Show that Inxax = xinx - x + c, where c is a constant. (iii) Using integration by parts, or otherwise, find the exact value of the area of the shaded region between the curve, the x-axis and the normal PQ. UI 4 Find the exact value of 0 sin 50de. 14] 5 A curve has equation y = In(1 + 3 cos2 x) for O s x 6 5x. dx (1) Express - in terms of tan.x. 141 (ii) Hence find the x-coordinate of the point on the curve where the gradient is -1. Give your answer correct to 3 significant figures. (2]