sum OF the roots

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\\\textsl{let N be sum of all the roots of the equation }\left (\frac{1}{2x} -1 \right )^{2009}=-1\\ \textit{find the last digit of N}

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xYz ·2010-03-04 20:46:58

\left(2x-1 \right)^{2009}=(2x)^{2009} \\ (2x)^{2009}-2009(2x)^{2008}+\binom{2009}{2}(2x)^{2007}-...=(2x)^{2009} \\ \text{sum of roots is } \\ \\ \frac{\binom{2009}{2}}{2009.2} =502 \\\\\text{so ur answer should be 2}

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Rasheed Ahmed ·2010-03-04 23:10:40

thanks xyz :)

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sum OF the roots

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