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Question Number 51843 Answers: 1 Comments: 3

If ax^2 +bx+c+i=0 has purely imaginary roots where a,b,c are non−zero real. answer given: a=b^2 c I think question is wrong since if z_1 and z_2 are roots than z_1 +z_2 =−(b/a) purely imaginary=purely real not possible Can some point a mistake.

$${If}\:{ax}^{\mathrm{2}} +{bx}+{c}+{i}=\mathrm{0}\:\mathrm{has}\:\mathrm{purely} \\ $$$$\mathrm{imaginary}\:\mathrm{roots}\:\mathrm{where}\: \\ $$$${a},{b},{c}\:{are}\:{non}−{zero}\:{real}. \\ $$$${answer}\:{given}:\:{a}={b}^{\mathrm{2}} {c} \\ $$$$ \\ $$$$\mathrm{I}\:\mathrm{think}\:\mathrm{question}\:\mathrm{is}\:\mathrm{wrong} \\ $$$$\mathrm{since}\:\mathrm{if}\:{z}_{\mathrm{1}} \:\mathrm{and}\:{z}_{\mathrm{2}} \:\mathrm{are}\:\mathrm{roots}\:\mathrm{than} \\ $$$${z}_{\mathrm{1}} +{z}_{\mathrm{2}} =−\frac{{b}}{{a}} \\ $$$${purely}\:{imaginary}={purely}\:{real} \\ $$$${not}\:{possible} \\ $$$$\mathrm{Can}\:\mathrm{some}\:\mathrm{point}\:\mathrm{a}\:\mathrm{mistake}. \\ $$

Question Number 51841 Answers: 0 Comments: 2

Question Number 51840 Answers: 2 Comments: 0

solve (dy/(dx )) + ((2y)/(3x )) = (x/(√y))

$${solve} \\ $$$$\frac{{dy}}{{dx}\:}\:+\:\frac{\mathrm{2}{y}}{\mathrm{3}{x}\:}\:=\:\frac{{x}}{\sqrt{{y}}} \\ $$

Question Number 51837 Answers: 1 Comments: 1

Question Number 51834 Answers: 0 Comments: 1

calculatef(a)= ∫_0 ^∞ ((ln(1+at^2 ))/(1+t^4 ))dt with a>0. 2)find the value of ∫_0 ^∞ ((ln(3+t^2 ))/(1+t^4 ))dt.

$${calculatef}\left({a}\right)=\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{ln}\left(\mathrm{1}+{at}^{\mathrm{2}} \right)}{\mathrm{1}+{t}^{\mathrm{4}} }{dt}\:\:{with}\:{a}>\mathrm{0}. \\ $$$$\left.\mathrm{2}\right){find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{ln}\left(\mathrm{3}+{t}^{\mathrm{2}} \right)}{\mathrm{1}+{t}^{\mathrm{4}} }{dt}. \\ $$

Question Number 51825 Answers: 1 Comments: 3

find f(α)=∫_0 ^1 ln(1+e^(−α) x)dx with α≥0

$${find}\:{f}\left(\alpha\right)=\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\mathrm{1}+{e}^{−\alpha} {x}\right){dx}\:\:{with}\:\alpha\geqslant\mathrm{0} \\ $$

Question Number 51824 Answers: 1 Comments: 0

find ∫ (dx/(cosx +cos(2x)+cos(3x)))

$${find}\:\int\:\:\:\frac{{dx}}{{cosx}\:+{cos}\left(\mathrm{2}{x}\right)+{cos}\left(\mathrm{3}{x}\right)} \\ $$

Question Number 51818 Answers: 0 Comments: 0

Find the relation between the ecentric angles of the point which are at the end of focal chord

$${Find}\:{the}\:{relation}\:{between} \\ $$$${the}\:{ecentric}\:{angles} \\ $$$${of}\:{the}\:{point}\:\:{which}\:{are} \\ $$$${at}\:{the}\:{end}\:{of}\:{focal}\:{chord} \\ $$

Question Number 51817 Answers: 0 Comments: 0

The earth moves arround the sun in an elliptical orbit with the sun at one of its foci.the eccentricity (1/3).the shortest distance from the earth to sun is 3000000km.Find the furthest distance of the earth from the sun.

$${The}\:{earth}\:{moves}\:{arround} \\ $$$${the}\:{sun}\:{in}\:{an}\:{elliptical} \\ $$$${orbit}\:{with}\:{the}\:{sun}\:{at} \\ $$$${one}\:{of}\:{its}\:{foci}.{the}\:{eccentricity} \\ $$$$\frac{\mathrm{1}}{\mathrm{3}}.{the}\:{shortest}\:{distance} \\ $$$${from}\:{the}\:{earth}\:{to}\:{sun}\: \\ $$$${is}\:\mathrm{3000000}{km}.{Find}\:{the} \\ $$$${furthest}\:{distance}\:{of}\:{the} \\ $$$${earth}\:{from}\:{the}\:{sun}. \\ $$

Question Number 51812 Answers: 0 Comments: 4

Question Number 51805 Answers: 2 Comments: 3

Question Number 51798 Answers: 0 Comments: 3

Question Number 51779 Answers: 0 Comments: 3

Q= In how many ways 8 students can be divided into two equal groups? Ans= ((8!)/(2!×(4!)^2 )) here why two factorial is divided? we do not do the same incase of distributing 52 cards equally among 4 persons. pls explain...

$${Q}=\:\:{In}\:{how}\:{many}\:{ways}\:\mathrm{8}\:{students}\:{can}\:{be}\:{divided}\:{into}\:{two}\:{equal}\:{groups}? \\ $$$$ \\ $$$${Ans}=\:\:\:\:\frac{\mathrm{8}!}{\mathrm{2}!×\left(\mathrm{4}!\right)^{\mathrm{2}} }\:\:\: \\ $$$$ \\ $$$${here}\:{why}\:{two}\:{factorial}\:{is}\:{divided}? \\ $$$${we}\:{do}\:{not}\:{do}\:{the}\:{same}\:{incase}\:{of}\:{distributing}\:\mathrm{52}\:{cards}\:{equally}\:{among}\:\mathrm{4}\:{persons}. \\ $$$$ \\ $$$${pls}\:{explain}... \\ $$

Question Number 51774 Answers: 1 Comments: 4