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let-give-p-x-x-j-n-x-j-n-with-j-e-i-2pi-3-1-find-roots-of-p-x-2-factorize-inside-C-x-p-x-3-factorize-inside-R-x-p-x-




Question Number 31495 by abdo imad last updated on 09/Mar/18
let give p(x)=(x+j)^n  −(x−j)^n  with j=e^(i((2π)/3))   1) find roots of p(x)  2) factorize inside C[ x] p(x)  3)factorize inside R[x] p(x).
$${let}\:{give}\:{p}\left({x}\right)=\left({x}+{j}\right)^{{n}} \:−\left({x}−{j}\right)^{{n}} \:{with}\:{j}={e}^{{i}\frac{\mathrm{2}\pi}{\mathrm{3}}} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{roots}\:{of}\:{p}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{factorize}\:{inside}\:{C}\left[\:{x}\right]\:{p}\left({x}\right) \\ $$$$\left.\mathrm{3}\right){factorize}\:{inside}\:{R}\left[{x}\right]\:{p}\left({x}\right). \\ $$

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