Question and Answers Forum

if f(x) = 3x^3 + px^2 + 4x − 8 and (x − 1) is a factor of f(x). a) find the value of p. with these value of p b) solve the equation f(x) = 0. if α and β are roots of f(x), c) find α + β and αβ d) Evaluate α^2 + β^2 hence α − β

$${if}\:{f}\left({x}\right)\:=\:\mathrm{3}{x}^{\mathrm{3}} \:+\:{px}^{\mathrm{2}} \:+\:\mathrm{4}{x}\:−\:\mathrm{8} \\ $$$${and}\:\left({x}\:−\:\mathrm{1}\right)\:{is}\:{a}\:{factor}\:{of}\: \\ $$$${f}\left({x}\right). \\ $$$$\left.{a}\right)\:{find}\:{the}\:{value}\:{of}\:{p}. \\ $$$${with}\:{these}\:{value}\:{of}\:{p} \\ $$$$\left.{b}\right)\:{solve}\:{the}\:{equation}\:{f}\left({x}\right)\:=\:\mathrm{0}. \\ $$$${if}\:\alpha\:{and}\:\beta\:{are}\:{roots}\:{of}\: \\ $$$${f}\left({x}\right),\: \\ $$$$\left.{c}\right)\:{find}\:\alpha\:+\:\beta\:{and}\:\alpha\beta \\ $$$$\left.{d}\right)\:{Evaluate}\:\alpha^{\mathrm{2}} \:+\:\beta^{\mathrm{2}} \:{hence}\:\alpha\:−\:\beta \\ $$$$ \\ $$

Question Number 40139 Answers: 0 Comments: 3

let I_n = ∫_0 ^1 x^n (√(1−x)) dx 1) calculate I_0 and I_1 2) prove that ∀n∈ N^★ (3+2n) I_n =2n I_(n−1) 3) find I_n interms of n

$${let}\:\:{I}_{{n}} =\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:{x}^{{n}} \sqrt{\mathrm{1}−{x}}\:{dx} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{I}_{\mathrm{0}} \:\:{and}\:{I}_{\mathrm{1}} \\ $$$$\left.\mathrm{2}\right)\:{prove}\:{that}\:\:\forall{n}\in\:{N}^{\bigstar} \:\:\:\:\left(\mathrm{3}+\mathrm{2}{n}\right)\:{I}_{{n}} =\mathrm{2}{n}\:{I}_{{n}−\mathrm{1}} \\ $$$$\left.\mathrm{3}\right)\:{find}\:{I}_{{n}} \:\:{interms}\:{of}\:{n} \\ $$

Question Number 39814 Answers: 2 Comments: 0

kwame, ama and yaw shared an amount of money in the ratio 3:4:5. if ama had $8,400 more than kwame. find the total amount shared.

$$\mathrm{kwame},\:\mathrm{ama}\:\mathrm{and}\:\mathrm{yaw}\:\mathrm{shared}\:\mathrm{an}\:\mathrm{amount}\:\mathrm{of}\:\mathrm{money} \\ $$$$\mathrm{in}\:\mathrm{the}\:\mathrm{ratio}\:\mathrm{3}:\mathrm{4}:\mathrm{5}.\:\mathrm{if}\:\mathrm{ama}\:\mathrm{had}\:\$\mathrm{8},\mathrm{400}\:\mathrm{more}\:\mathrm{than}\:\mathrm{kwame}. \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{total}\:\mathrm{amount}\:\mathrm{shared}. \\ $$

Question Number 39811 Answers: 1 Comments: 1

Question Number 39799 Answers: 1 Comments: 0

what will be the number which makes 680621 a perfect square root?

$$\boldsymbol{\mathrm{what}}\:\boldsymbol{\mathrm{will}}\:\boldsymbol{\mathrm{be}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{number}}\:\boldsymbol{\mathrm{which}}\:\boldsymbol{\mathrm{makes}}\:\mathrm{680621} \\ $$$$\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{perfect}}\:\boldsymbol{\mathrm{square}}\:\boldsymbol{\mathrm{root}}? \\ $$

Question Number 39798 Answers: 0 Comments: 5

Please someone should propose a textbook that really explains Gauss law,electric flux and capacitance.I need to download 1.. Thanks.

$${Please}\:{someone}\:{should}\:{propose}\:{a} \\ $$$${textbook}\:{that}\:{really}\:{explains} \\ $$$${Gauss}\:{law},{electric}\:{flux}\:{and} \\ $$$${capacitance}.{I}\:{need}\:{to}\:{download}\:\mathrm{1}.. \\ $$$${Thanks}. \\ $$

Question Number 39794 Answers: 1 Comments: 0

Two charged concentric spheres have radii of 10cm and 18cm.The charge on the inner sphere is 6.0×10^(−8) C and that on the outer sphere is 2.0×10^(−8) C.Find the electric field (i)at r=12cm and (ii)at r=25cm

$${Two}\:{charged}\:{concentric}\:{spheres} \\ $$$${have}\:{radii}\:{of}\:\mathrm{10}{cm}\:{and}\:\mathrm{18}{cm}.{The} \\ $$$${charge}\:{on}\:{the}\:{inner}\:{sphere}\:{is} \\ $$$$\mathrm{6}.\mathrm{0}×\mathrm{10}^{−\mathrm{8}} {C}\:{and}\:{that}\:{on}\:{the}\:{outer} \\ $$$${sphere}\:{is}\:\mathrm{2}.\mathrm{0}×\mathrm{10}^{−\mathrm{8}} {C}.{Find}\:{the} \\ $$$${electric}\:{field}\:\left({i}\right){at}\:{r}=\mathrm{12}{cm}\:{and} \\ $$$$\left({ii}\right){at}\:{r}=\mathrm{25}{cm} \\ $$$$ \\ $$$$ \\ $$

Question Number 39792 Answers: 1 Comments: 1

A positive charge of magnigude 2.5μC is at the centre of an uncharged spherical conducting shell of inner radius 60cm and an outer radius of 90cm. (i)find the charge densities on thd inner and outer surfaces of the shell and the total charge on each surface. ii)find the electricity field everywhere.

$${A}\:{positive}\:{charge}\:{of}\:{magnigude} \\ $$$$\mathrm{2}.\mathrm{5}\mu{C}\:{is}\:{at}\:{the}\:{centre}\:{of}\:{an}\:{uncharged} \\ $$$${spherical}\:{conducting}\:{shell}\:{of}\:{inner} \\ $$$${radius}\:\mathrm{60}{cm}\:{and}\:{an}\:{outer}\:{radius} \\ $$$${of}\:\mathrm{90}{cm}. \\ $$$$\left({i}\right){find}\:{the}\:{charge}\:{densities}\:{on}\:{thd} \\ $$$${inner}\:{and}\:{outer}\:{surfaces}\:{of}\:{the} \\ $$$${shell}\:{and}\:{the}\:{total}\:{charge}\:{on}\:{each} \\ $$$${surface}. \\ $$$$\left.{ii}\right){find}\:{the}\:{electricity}\:{field} \\ $$$${everywhere}. \\ $$

Question Number 39787 Answers: 0 Comments: 2

calculste I_λ = ∫_(−∞) ^(+∞) ((cos(λx^n ))/(1+x^2 )) dx with λ from R and n integr natural 2) find the vslue of ∫_(−∞) ^(+∞) ((cos(3 x^9 ))/(1+x^2 )) dx .

$${calculste}\:\:{I}_{\lambda} \:=\:\int_{−\infty} ^{+\infty} \:\:\frac{{cos}\left(\lambda{x}^{{n}} \right)}{\mathrm{1}+{x}^{\mathrm{2}} }\:{dx}\:\:{with} \\ $$$$\lambda\:{from}\:{R}\:{and}\:{n}\:{integr}\:{natural} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{vslue}\:{of}\:\:\int_{−\infty} ^{+\infty} \:\:\frac{{cos}\left(\mathrm{3}\:{x}^{\mathrm{9}} \right)}{\mathrm{1}+{x}^{\mathrm{2}} }\:{dx}\:. \\ $$

Question Number 39783 Answers: 1 Comments: 0

Find roots of f(x)=x^4 −10x^3 +35x^2 −50x+24

$${Find}\:{roots}\:{of} \\ $$$${f}\left({x}\right)={x}^{\mathrm{4}} −\mathrm{10}{x}^{\mathrm{3}} +\mathrm{35}{x}^{\mathrm{2}} −\mathrm{50}{x}+\mathrm{24} \\ $$

Question Number 39779 Answers: 1 Comments: 0

f(x)=x^4 −2x^3 +3x^2 −4x+5 Find the roots.

$${f}\left({x}\right)={x}^{\mathrm{4}} −\mathrm{2}{x}^{\mathrm{3}} +\mathrm{3}{x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{5} \\ $$$${Find}\:{the}\:{roots}. \\ $$

Question Number 39776 Answers: 0 Comments: 3