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if-a-and-b-are-the-root-of-the-quadratic-equation-x-2-2x-3-then-find-the-value-of-2-2-

Question Number 25184 by lucky singh last updated on 05/Dec/17 $${if}\:{a}\:{and}\:{b}\:{are}\:{the}\:{root}\:{of}\:{the}\:{quadratic}\:{equation}\:{x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{3}\:{then}\:{find}\:{the}\:{value}\:{of}\:\alpha^{\mathrm{2}} /\beta+\beta^{\mathrm{2}} /\alpha \\ $$ Commented by prakash jain last updated on 05/Dec/17 $${x}^{\mathrm{2}}…

Given-a-rational-function-f-x-ax-2-bx-c-x-q-has-minimum-point-at-2-9-and-maximum-point-at-2-1-Find-value-of-a-b-c-and-q-

Question Number 156188 by naka3546 last updated on 09/Oct/21 $${Given}\:\:{a}\:\:{rational}\:\:{function} \\ $$$$\:\:\:\:\:{f}\left({x}\right)\:=\:\:\frac{{ax}^{\mathrm{2}} +{bx}+{c}}{{x}+{q}} \\ $$$${has}\:\:{minimum}\:\:{point}\:\:{at}\:\left(−\mathrm{2},\mathrm{9}\right)\:\:{and}\:\:{maximum}\:\:{point}\:\:{at}\:\:\left(\mathrm{2},\mathrm{1}\right)\:. \\ $$$${Find}\:\:{value}\:\:{of}\:\:{a},\:{b},\:{c},\:\:{and}\:\:{q}\:. \\ $$ Commented by MJS_new last updated on…

find-the-infinite-sum-n-0-F-n-2-n-where-F-n-1-5-1-5-2-n-1-1-5-1-5-2-n-1-

Question Number 90609 by Maclaurin Stickker last updated on 25/Apr/20 $${find}\:{the}\:{infinite}\:{sum}\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{{F}_{{n}} }{\mathrm{2}^{{n}} }\: \\ $$$${where}\:{F}_{{n}} =\frac{\mathrm{1}}{\:\sqrt{\mathrm{5}}}\left(\frac{\mathrm{1}+\sqrt{\mathrm{5}}}{\mathrm{2}}\right)^{{n}+\mathrm{1}} −\frac{\mathrm{1}}{\:\sqrt{\mathrm{5}}}\left(\frac{\mathrm{1}−\sqrt{\mathrm{5}}}{\mathrm{2}}\right)^{{n}+\mathrm{1}} \\ $$ Commented by abdomathmax last…