Question and Answers Forum

Determine a relation between the coefficients a, b, c, d such that the equation: ax^3 +bx^2 +cx+d=0 has three real roots (with a pair of double roots).

$${Determine}\:{a}\:{relation}\:{between}\:\:{the} \\ $$$${coefficients}\:\:\boldsymbol{{a}},\:\boldsymbol{{b}},\:\boldsymbol{{c}},\:\boldsymbol{{d}}\:{such}\:{that}\:{the} \\ $$$${equation}:\:\:{ax}^{\mathrm{3}} +{bx}^{\mathrm{2}} +{cx}+{d}=\mathrm{0} \\ $$$${has}\:{three}\:{real}\:{roots}\:\left({with}\:{a}\:{pair}\right. \\ $$$$\left.{of}\:{double}\:{roots}\right). \\ $$

Question Number 20239 Answers: 1 Comments: 0

∫(((2x+3)dx)/(√(x^2 +4x−7)))

$$\int\frac{\left(\mathrm{2}{x}+\mathrm{3}\right){dx}}{\sqrt{{x}^{\mathrm{2}} +\mathrm{4}{x}−\mathrm{7}}} \\ $$

Question Number 20238 Answers: 1 Comments: 1

∫(dx/(x^2 −x+1))

$$\int\frac{{dx}}{{x}^{\mathrm{2}} −{x}+\mathrm{1}} \\ $$

Question Number 20237 Answers: 0 Comments: 1

∫(e^(tan^(−1) x) /(1+x^2 ))dx

$$\int\frac{{e}^{\mathrm{tan}^{−\mathrm{1}} {x}} }{\mathrm{1}+{x}^{\mathrm{2}} }{dx} \\ $$

Question Number 20235 Answers: 0 Comments: 1

if t_((m+1)) =2t_((n+1)) so proof t_((3m+1)) =2t_((m+n+1) ) help please.........

$$ \\ $$$${if}\:\:\:\:\:\:\:\:{t}_{\left({m}+\mathrm{1}\right)} =\mathrm{2}{t}_{\left({n}+\mathrm{1}\right)} \\ $$$${so}\:{proof} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{t}_{\left(\mathrm{3}{m}+\mathrm{1}\right)} =\mathrm{2}{t}_{\left({m}+{n}+\mathrm{1}\right)\:\:\:\:\:\:} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{help}\:{please}......... \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 20230 Answers: 1 Comments: 5

Question Number 20217 Answers: 0 Comments: 1

Question Number 20205 Answers: 1 Comments: 0

find the sin^(−1) diferentiation

$${find}\:{the}\:{sin}^{−\mathrm{1}} \:{diferentiation} \\ $$

Question Number 20204 Answers: 0 Comments: 0

Question Number 20203 Answers: 0 Comments: 1

Question Number 20201 Answers: 2 Comments: 0

^4 (√(49 − 20(√6))) =

$$\:^{\mathrm{4}} \sqrt{\mathrm{49}\:−\:\mathrm{20}\sqrt{\mathrm{6}}}\:= \\ $$

Question Number 20200 Answers: 1 Comments: 0

Question Number 20198 Answers: 1 Comments: 0

Find exact form of cos (tan^(−1) ((1/2)))

$$\mathrm{Find}\:\mathrm{exact}\:\mathrm{form}\:\mathrm{of} \\ $$$$\mathrm{cos}\:\left(\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{1}}{\mathrm{2}}\right)\right) \\ $$

Question Number 20195 Answers: 1 Comments: 0

Question Number 20194 Answers: 0 Comments: 5

A plane is drawn through the midpoint of a diagonal of a cube perpendicular to the diagonal. Determine the area of the figure resulting from the section of the cube cut by this plane if the edge of the cube is equal to a.

$${A}\:{plane}\:{is}\:{drawn}\:{through}\:{the}\: \\ $$$${midpoint}\:{of}\:{a}\:{diagonal}\:{of}\:{a}\:{cube} \\ $$$${perpendicular}\:{to}\:{the}\:{diagonal}. \\ $$$${Determine}\:{the}\:{area}\:{of}\:{the}\:{figure} \\ $$$${resulting}\:{from}\:{the}\:{section}\:{of}\:{the} \\ $$$${cube}\:{cut}\:{by}\:{this}\:{plane}\:{if}\:{the}\:{edge} \\ $$$${of}\:{the}\:{cube}\:{is}\:{equal}\:{to}\:\boldsymbol{{a}}. \\ $$

Question Number 20192 Answers: 0 Comments: 0

t_1 =3, t_n =3t_(n−1) +2 ....n>1

$$ \\ $$$${t}_{\mathrm{1}} =\mathrm{3},\:{t}_{{n}} =\mathrm{3}{t}_{{n}−\mathrm{1}} +\mathrm{2}\:\:\:\:\:....{n}>\mathrm{1} \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 20202 Answers: 0 Comments: 10

Is definite integral can have negative value? Because I think ∫_a ^b f(x) dx is total area below graph f(x) from x = a until x = b, so it can′t be negative

$$\mathrm{Is}\:\mathrm{definite}\:\mathrm{integral}\:\mathrm{can}\:\mathrm{have}\:\mathrm{negative}\:\mathrm{value}? \\ $$$$\mathrm{Because}\:\mathrm{I}\:\mathrm{think}\:\int_{{a}} ^{{b}} {f}\left({x}\right)\:{dx}\:\mathrm{is}\:\mathrm{total}\:\mathrm{area}\:\mathrm{below} \\ $$$$\mathrm{graph}\:{f}\left({x}\right)\:\mathrm{from}\:{x}\:=\:{a}\:\mathrm{until}\:{x}\:=\:{b},\:\mathrm{so}\:\mathrm{it}\:\mathrm{can}'\mathrm{t} \\ $$$$\mathrm{be}\:\mathrm{negative} \\ $$

Question Number 20182 Answers: 0 Comments: 0

Question Number 20187 Answers: 0 Comments: 1

t_n =(t_(n−1) /n^2 ), t_1 =3;t_2 ,t_3 ,(n≥2)

$${t}_{{n}} =\frac{{t}_{{n}−\mathrm{1}} }{{n}^{\mathrm{2}} },\:{t}_{\mathrm{1}} =\mathrm{3};{t}_{\mathrm{2}} ,{t}_{\mathrm{3}} ,\left({n}\geqslant\mathrm{2}\right) \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

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