Question Number 98924 by Rio Michael last updated on 17/Jun/20 $$\mathrm{Prove}\:\mathrm{that}\:\mathrm{if}\:{a}+\:{bi}\:\mathrm{is}\:\mathrm{a}\:\mathrm{root}\:\mathrm{to} \\ $$$$\:{pz}^{\mathrm{2}} \:+\:{qz}\:+\:{r}\:=\:\mathrm{0}\:,\:\mathrm{where}\:{a},{b},{p},{q},{r}\:\in\mathbb{R} \\ $$$$\mathrm{then}\:{a}−{bi}\:\mathrm{is}\:\mathrm{also}\:\mathrm{a}\:\mathrm{root}\:\mathrm{to}\:\mathrm{that}\:\mathrm{equation}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 164447 by LEKOUMA last updated on 17/Jan/22 Answered by Mathspace last updated on 17/Jan/22 $${f}\left({x}\right)=\frac{{e}^{{ln}^{\mathrm{2}} {x}} }{{e}^{{xln}\left({lnx}\right)} }={e}^{{ln}^{\mathrm{2}} {x}−{xln}\left({lnx}\right)} \\ $$$${u}\left({x}\right)={ln}^{\mathrm{2}} {x}−{xln}\left({lnx}\right)=_{{lnx}={t}} \\…
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Question Number 33322 by Rio Mike last updated on 15/Apr/18 $$\left.{a}\right)\:{px}^{\mathrm{2}} +\:\mathrm{3}{x}\:+\:{q}=\mathrm{0}\:{has}\:{roots}\: \\ $$$$\:\:\left[\frac{\alpha+\beta}{\alpha\beta}\right]×\:\alpha\beta \\ $$$${find}\:{p}\:{and}\:{q}\:{if}\: \\ $$$$\:\:{x}^{\mathrm{2}} −\:\mathrm{7}{x}\:+\:\mathrm{4}\:=\:\mathrm{0}\:{with}\:{real}\:{and}\: \\ $$$${distinct}\:{roots}\:{has}\:{same}\:{roots}.. \\ $$$$\left.{b}\right){if}\:\alpha\:{and}\:\beta\:{are}\:{roots}\:{of}\: \\ $$$$\:{x}^{\mathrm{2}}…
Question Number 33255 by Rio Mike last updated on 13/Apr/18 $${if}\:{the}\:{roots}\:{of}\:{the}\:{equation}\: \\ $$$$\:\:\mathrm{3}{x}^{\mathrm{2}} +\mathrm{5}{x}+\mathrm{2}=\mathrm{0}\:{are}\:\left(\alpha+\beta\right)\left(\alpha\beta\right) \\ $$$${then}\:{the}\:{value}\:{of}\:{p}\:{if}\:{x}^{\mathrm{2}} +\:{px}\:−\:\mathrm{6}=\mathrm{0} \\ $$$${is}? \\ $$ Commented by Rio Mike…
Question Number 33252 by Rio Mike last updated on 13/Apr/18 $${if}\:\alpha\:{and}\:\beta\:{are}\:{roots}\:{of}\:{the}\:{equation} \\ $$$$\:{x}^{\mathrm{2}} +{px}\:+\:{q}=\mathrm{0} \\ $$$${then}\:{the}\:{value}\:{p}\:{and}\:{q}\:{when}\: \\ $$$$\:\:{x}^{\mathrm{2}} +\:\mathrm{3}{x}\:+\:\mathrm{2}=\mathrm{0}\:{has}\:{same}\:{roots}\:{are}? \\ $$ Commented by Rasheed.Sindhi last…
Question Number 33230 by Rio Mike last updated on 13/Apr/18 $${how}\:{many}\:{ways}\:{can}\:{the}\:{word}\: \\ $$$$\:\:\:\:{MOGGOMBABA}\: \\ $$$${be}\:{arranged}\:{hence}\:{find}\:{S}_{\infty} \:{of}\:{a}\: \\ $$$${sequence}\:{a},{ar},{ar}^{\mathrm{2}} \:{in}\:{integral}\: \\ $$$$\:\:\mathrm{1},\sqrt{\mathrm{2}}\:,\:\mathrm{2},… \\ $$ Answered by…
Question Number 33211 by abdo imad last updated on 12/Apr/18 $${find}\:{lim}_{{x}\rightarrow+\infty} \:\:\:{x}\:{e}^{−{x}^{\mathrm{2}} } \:\:\int_{{x}−\mathrm{1}} ^{{x}} \:{e}^{{t}^{\mathrm{2}} } {dt}\:. \\ $$ Terms of Service Privacy Policy…
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Question Number 33185 by Rio Mike last updated on 12/Apr/18 $${find}\:{k}\:{if} \\ $$$$\:\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left(\mathrm{2}{k}\right)\left(\mathrm{2}\right)^{{n}−\mathrm{1}} =\mathrm{64} \\ $$$${hence}\:{find}\:{k}\:{if}\:\:{kx}^{\mathrm{2}} +\mathrm{3}{x}\:+\mathrm{4}=\mathrm{0}\:{has} \\ $$$${real}\:{roots}. \\ $$ Answered by…