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Category: Algebra

if-f-x-2x-2-12x-10-i-sketch-the-graph-of-y-f-x-for-1-x-7-ii-find-the-set-of-values-of-k-for-which-the-equation-f-x-k-has-4-distinct-roots-

Question Number 113854 by ayenisamuel last updated on 15/Sep/20 $${if}\:{f}\left({x}\right)=\mathrm{2}{x}^{\mathrm{2}} −\mathrm{12}{x}+\mathrm{10}.\: \\ $$$$\left({i}\right)\:{sketch}\:{the}\:{graph}\:{of}\:{y}=\mid{f}\left({x}\right)\mid\:{for} \\ $$$$−\mathrm{1}\leqslant{x}\leqslant\mathrm{7}. \\ $$$$\left({ii}\right)\:{find}\:{the}\:{set}\:{of}\:{values}\:{of}\:{k}\:{for} \\ $$$${which}\:{the}\:{equation}\:\mid{f}\left({x}\right)\mid={k}\:{has}\:\mathrm{4} \\ $$$${distinct}\:{roots}. \\ $$ Answered by…

x-2-4x-1-9-

Question Number 48306 by Messias last updated on 21/Nov/18 $$\mathrm{x}^{\mathrm{2}} +\mathrm{4x}+\mathrm{1}=\mathrm{9} \\ $$ Answered by MJS last updated on 21/Nov/18 $${x}^{\mathrm{2}} +{px}+{q}=\mathrm{0}\:\Rightarrow\:{x}=−\frac{{p}}{\mathrm{2}}\pm\sqrt{\frac{{p}^{\mathrm{2}} }{\mathrm{4}}−{q}} \\ $$$$\mathrm{in}\:\mathrm{this}\:\mathrm{case}:\:{p}=\mathrm{4};\:{q}=−\mathrm{8}…

Question-48294

Question Number 48294 by behi83417@gmail.com last updated on 21/Nov/18 Commented by MJS last updated on 22/Nov/18 $${x}^{\mathrm{6}} +{x}^{\mathrm{5}} +{x}^{\mathrm{4}} −\mathrm{10}{x}^{\mathrm{3}} +{x}^{\mathrm{2}} +{x}+\mathrm{1}=\mathrm{0} \\ $$$${x}=\mathrm{tan}\:\frac{{t}}{\mathrm{2}} \\…

f-x-1-x-1-x-fofofo-of-2004-x-

Question Number 179336 by mathlove last updated on 28/Oct/22 $${f}\left({x}\right)=\frac{\mathrm{1}−{x}}{\mathrm{1}+{x}} \\ $$$$\left(\underset{\mathrm{2004}} {\underbrace{{fofofo}……..{of}}}\right)_{{x}} =? \\ $$ Commented by a.lgnaoui last updated on 28/Oct/22 $${fof}\left({x}\right)=\frac{\mathrm{1}−\frac{\mathrm{1}−{x}}{\mathrm{1}+{x}}}{\mathrm{1}+\frac{\mathrm{1}−{x}}{\mathrm{1}+{x}}}=\frac{\mathrm{2}{x}}{\mathrm{2}}={x}\:\:\left({ordre}\:\mathrm{2}\right) \\…

what-is-the-number-that-is-evenly-divisible-by-3-and-6-and-but-not-divisible-by-2-

Question Number 113801 by Study last updated on 15/Sep/20 $${what}\:{is}\:{the}\:{number}\:{that}\:{is}\:{evenly}\: \\ $$$${divisible}\:{by}\:\mathrm{3}\:{and}\:\mathrm{6}\:{and}\:{but}\:{not}\:{divisible} \\ $$$${by}\:\mathrm{2}? \\ $$ Commented by MJS_new last updated on 15/Sep/20 $$\mathrm{6}\mid{x}\:\Rightarrow\:\mathrm{3}\mid{x}\:\wedge\:\mathrm{2}\mid{x} \\…

Question-179338

Question Number 179338 by mathlove last updated on 28/Oct/22 Answered by Acem last updated on 28/Oct/22 $$=\:\mathrm{20}×\:−\:\frac{\mathrm{5}}{\mathrm{3}}\:=\:−\:\frac{\mathrm{100}}{\mathrm{3}}\: \\ $$$${if}\:\mathrm{20}\:{was}\:{num}.\:{of}\:{relation}, \\ $$$$\:{the}\:{answer}\:{is}\:−\:\frac{\mathrm{5}}{\mathrm{3}} \\ $$ Commented by…