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Category: Algebra

Let-a-i-1-i-10-be-the-roots-of-the-equation-m-1-10-mx-m-0-Prove-that-100-i-1-10-a-i-2-1-61-An-algebra-question-as-seen-on-Brilliant-

Question Number 3775 by Yozzii last updated on 20/Dec/15 $${Let}\:{a}_{{i}} \:\left(\mathrm{1}\leqslant{i}\leqslant\mathrm{10}\right)\:{be}\:{the}\:{roots}\:{of}\:{the} \\ $$$${equation}\:\underset{{m}=\mathrm{1}} {\overset{\mathrm{10}} {\sum}}{mx}^{{m}} =\mathrm{0}.\:{Prove}\:{that} \\ $$$$\mathrm{100}\underset{{i}=\mathrm{1}} {\overset{\mathrm{10}} {\prod}}\left({a}_{{i}} ^{\mathrm{2}} +\mathrm{1}\right)=\mathrm{61}. \\ $$$$\left({An}\:{algebra}\:{question}\:{as}\:{seen}\:{on}\:{Brilliant}.\right) \\…

Question-69297

Question Number 69297 by ajfour last updated on 22/Sep/19 Commented by ajfour last updated on 22/Sep/19 $${If}\:{the}\:{graph}\:{is}\:{a}\:{cubic} \\ $$$$\:\:\:\:{y}={x}^{\mathrm{3}} +{ax}^{\mathrm{2}} +{bx}+{c} \\ $$$${find}\:{point}\:{of}\:{intersection}\:{of} \\ $$$${the}\:{red}\:{and}\:{blue}\:{lines}.…

Question-69293

Question Number 69293 by A8;15: last updated on 22/Sep/19 Commented by MJS last updated on 22/Sep/19 $$\mathrm{great},\:\mathrm{you}'\mathrm{ve}\:\mathrm{been}\:\mathrm{faster}\:\mathrm{than}\:\mathrm{me} \\ $$$$\mathrm{but}\:\mathrm{also}\:{x}=\mathrm{0}\:\mathrm{is}\:\mathrm{a}\:\mathrm{solution} \\ $$ Commented by Rasheed.Sindhi last…

f-x-k-1-n-x-k-1-find-the-values-of-x-such-that-f-x-is-minumum-2-fund-the-roots-of-f-x-m-0-as-example-you-can-set-n-100-m-2500-

Question Number 69276 by mr W last updated on 22/Sep/19 $${f}\left({x}\right)=\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\mid{x}+{k}\mid \\ $$$$\left(\mathrm{1}\right)\:{find}\:{the}\:{values}\:{of}\:{x}\:{such}\:{that}\:{f}\left({x}\right)\: \\ $$$${is}\:{minumum}. \\ $$$$\left(\mathrm{2}\right)\:{fund}\:{the}\:{roots}\:{of}\:{f}\left({x}\right)−{m}=\mathrm{0} \\ $$$$ \\ $$$${as}\:{example}\:{you}\:{can}\:{set}\:{n}=\mathrm{100},\:{m}=\mathrm{2500}. \\ $$…