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Author: Tinku Tara

The-roots-of-the-equation-x-2-m-3-x-m-0-are-such-that-exactly-one-of-them-lies-in-the-interval-1-2-Then-A-5-lt-m-lt-7-B-m-lt-10-C-2-lt-m-lt-5-

Question Number 140969 by EnterUsername last updated on 14/May/21 $$\mathrm{The}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{x}^{\mathrm{2}} −\left({m}−\mathrm{3}\right)\mathrm{x}+{m}=\mathrm{0}\:\mathrm{are} \\ $$$$\mathrm{such}\:\mathrm{that}\:\mathrm{exactly}\:\mathrm{one}\:\mathrm{of}\:\mathrm{them}\:\mathrm{lies}\:\mathrm{in}\:\mathrm{the}\:\mathrm{interval} \\ $$$$\left(\mathrm{1},\:\mathrm{2}\right).\:\mathrm{Then} \\ $$$$\left(\mathrm{A}\right)\:\mathrm{5}<{m}<\mathrm{7}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{B}\right)\:{m}<\mathrm{10} \\ $$$$\left(\mathrm{C}\right)\:\mathrm{2}<{m}<\mathrm{5}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{D}\right)\:{m}>\mathrm{10} \\ $$ Terms of Service Privacy…

If-a-0-and-a-l-m-2-2blm-c-0-and-a-l-n-2-2bln-c-0-then-A-mn-l-2-c-a-B-lm-n-2-c-a-C-ln-m-2-c-a-D-mn-l-2-bc-a-

Question Number 140965 by EnterUsername last updated on 14/May/21 $$\mathrm{If}\:{a}\neq\mathrm{0}\:\mathrm{and}\:{a}\left({l}+{m}\right)^{\mathrm{2}} +\mathrm{2}{blm}+{c}=\mathrm{0}\:\mathrm{and}\:{a}\left({l}+{n}\right)^{\mathrm{2}} + \\ $$$$\mathrm{2}{bln}+{c}=\mathrm{0},\:\mathrm{then} \\ $$$$\left(\mathrm{A}\right)\:{mn}={l}^{\mathrm{2}} +{c}/{a}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{B}\right)\:{lm}={n}^{\mathrm{2}} +{c}/{a} \\ $$$$\left(\mathrm{C}\right)\:{ln}={m}^{\mathrm{2}} +{c}/{a}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{D}\right)\:{mn}={l}^{\mathrm{2}} +{bc}/{a} \\ $$ Terms…

nice-calculus-if-n-0-cos-npi-2n-then-Re-

Question Number 140966 by mnjuly1970 last updated on 14/May/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…….{nice}……{calculus}….. \\ $$$$\:\:\:\:\:{if}\:\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\sqrt{{cos}\:\left({n}\pi\right)}\:}{\left(\mathrm{2}{n}\right)!!}\:=\:\omega \\ $$$$\:\:\:\:\:\:\:{then}\:\:\:{Re}\left(\omega\right):=?? \\ $$ Answered by Dwaipayan Shikari last updated on…