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Category: Algebra

1-factorizse-p-x-x-n-1-inside-C-x-2-find-the-value-of-k-1-n-1-sin-kpi-n-3-find-also-the-value-of-k-0-n-1-sin-kpi-n-

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Question Number 28370 by abdo imad last updated on 24/Jan/18 $$\left.\mathrm{1}\right)\:{factorizse}\:{p}\left({x}\right)\:={x}^{{n}} \:−\mathrm{1}\:\:{inside}\:{C}\left[{x}\right] \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\:\prod_{{k}=\mathrm{1}} ^{{n}−\mathrm{1}} \:{sin}\left(\frac{{k}\pi}{{n}}\right) \\ $$$$\left.\mathrm{3}\right){find}\:{also}\:{the}\:{value}\:{of}\:\:\:\:\prod_{{k}=\mathrm{0}} ^{{n}−\mathrm{1}} \:\:{sin}\left(\frac{{k}\pi}{{n}}\:+\theta\right). \\ $$ Commented by abdo…

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let-give-the-matrice-A-1-0-0-0-1-1-1-0-1-A-M-3-R-write-A-at-form-A-I-J-and-calcula

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Question Number 28369 by abdo imad last updated on 24/Jan/18 $${let}\:{give}\:{the}\:{matrice}\:\:\:{A}\:=\:\begin{pmatrix}{\mathrm{1}\:\:\:\:\:\:\mathrm{0}\:\:\:\:\:\:\mathrm{0}}\\{\mathrm{0}\:\:\:\:\:\:\:\mathrm{1}\:\:\:\:\:\:\mathrm{1}}\end{pmatrix} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left[\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{1}\:\:\:\:\:\:\:\:\mathrm{0}\:\:\:\:\:\:\mathrm{1}\right.\right. \\ $$$${A}\:\in\:{M}_{\mathrm{3}} \left({R}\right)\:\:{write}\:\:{A}\:{at}\:{form}\:\:{A}=\:{I}\:+{J}\:\:\:\:{and}\:{calculate} \\ $$$${A}^{{n}} . \\ $$ Terms of Service Privacy…

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P-is-apolynomial-from-C-n-x-having-n-roots-x-i-1-i-n-and-x-i-x-j-for-i-j-1-prove-that-i-1-n-1-p-x-i-0-2-find-i-1-n-x-i-k-p-x-i-with-k-

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Question Number 28368 by abdo imad last updated on 24/Jan/18 $${P}\:{is}\:{apolynomial}\:{from}\:{C}_{{n}} \left[{x}\right]\:{having}\:{n}\:{roots} \\ $$$$\left({x}_{{i}} \right)_{\mathrm{1}\leqslant{i}\leqslant{n}\:} \:\:\:\:{and}\:{x}_{{i}} #\:{x}_{{j}} \:{for}\:{i}#{j} \\ $$$$\left.\mathrm{1}\right)\:{prove}\:{that}\:\:\:\sum_{{i}=\mathrm{1}} ^{{n}} \:\:\:\frac{\mathrm{1}}{{p}^{'} \left({x}_{{i}} \right)}\:\:=\mathrm{0} \\…

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let-give-P-x-x-x-1-m-1-x-x-2-m-2-x-x-n-m-n-give-the-decomposition-of-F-x-d-P-P-d-mean-derivative-

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Question Number 28366 by abdo imad last updated on 24/Jan/18 $${let}\:{give}\:{P}\left({x}\right)=\:\alpha\left({x}−{x}_{\mathrm{1}} \right)^{{m}_{\mathrm{1}} } \left({x}−{x}_{\mathrm{2}} \right)^{{m}_{\mathrm{2}} } …..\left({x}−{x}_{{n}} \right)^{{m}_{{n}} } \\ $$$${give}\:{the}\:{decomposition}\:{of}\:{F}\left({x}\right)=\:\frac{{d}\left({P}\right)}{{P}}\:.{d}\:{mean}\:{derivative} \\ $$ Terms of…

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let-give-F-x-1-x-2-1-prove-that-P-n-Z-n-x-F-n-x-P-n-x-1-x-2-n-find-a-relation-of-recurence-between-the-P-n-prove-that-all-roots-of-P-n-are-reals-and-smples-

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Question Number 28364 by abdo imad last updated on 24/Jan/18 $${let}\:{give}\:{F}\left({x}\right)\:=\:\frac{\mathrm{1}}{{x}^{\mathrm{2}} +\mathrm{1}}\:{prove}\:{that}\:\exists\:{P}_{{n}} \in\:{Z}_{{n}} \left[{x}\right]\:/ \\ $$$${F}^{\left({n}\right)} \left({x}\right)=\:\:\frac{{P}_{{n}} \left({x}\right)}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{{n}} }\:\:\:{find}\:{a}\:{relation}\:{of}\:{recurence}\:{between}\: \\ $$$${the}\:\:{P}_{{n}} \:.{prove}\:{that}\:{all}\:{roots}\:{of}\:{P}_{{n}} \:{are}\:{reals}\:{and}\:{smples}. \\…

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