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    Complex numbers

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    1. The equation X^5 - 2X^4 - X^3 + 6X - 4 = 0 has a repeated root at X=1 and a root at X-2. By a process of division and solving a quadratic equation, find all the roots and hence write down all the factors of X^5 - 2X^4 - X^3 + 6X - 4

    2. Given that cosX= (e^jx + e^-jx)/2

    sinX= (e^jx - e^-jx)/2j

    using only this information, prove that 2cos5xsin2x = sin7x-sin3x

    Any help is would be greatly appreciated

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    Solution Preview

    Please find the solutions in the attached file.

    Solution to posting # 22309

    1. Given equation: X5 - 2X4 - X3+ 6X - 4 = 0
    Also given that (x-1) and (x-2) are solutions of the above equation. Performing long ...

    Solution Summary

    This shows how to find roots of a polynomial and how to verify a trigonometric statement