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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

https://brainmass.com/math/number-theory/complex-numbers-questions-22309

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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

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