Page 08 MARKS 17. The complex number z = 2 + i is a root of the polynomial equation 4 3 2 6 16 22 0 z z z z q − + − + = , where q∈]. (a) State a second root of the equation. (b) Find the value of q and the remaining roots. (c) Show the solutions to 4 3 2 6 16 22 0 z z z z q − + − + = on an Argand diagram. 18. The position of a particle at time t is given by the parametric equations x = t cos t, y = t sin t, t ≥ 0. (a) Find an expression for the instantaneous speed of the particle. The diagram below shows the path that the particle takes. y x A 0 (b) Calculate the instantaneous speed of the particle at point A. [END OF QUESTION PAPER] 1 6 1 5 2
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This question is part of the UK A-Level Mathematics syllabus. In the actual exam, structured questions typically require linking specific keywords to gain full marks. Applaa helps you drill these topics.
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