Question and Answers Forum

All Questions   Topic List

AlgebraQuestion and Answers: Page 324

Question Number 50924    Answers: 1   Comments: 0

factor the expression: E=x^5 +x^4 +1

$$\mathrm{factor}\:\mathrm{the}\:\mathrm{expression}: \\ $$$$\mathrm{E}={x}^{\mathrm{5}} +{x}^{\mathrm{4}} +\mathrm{1} \\ $$

Question Number 49647    Answers: 1   Comments: 3

let p(x) =x^(2n) −x^n +1 1) determine the roots of p(x) 2) factorize inside C[x] the polynom p(x) . 3)solve p(x)=0 and p(x) =2

$${let}\:{p}\left({x}\right)\:={x}^{\mathrm{2}{n}} \:−{x}^{{n}} \:+\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:{determine}\:{the}\:{roots}\:{of}\:{p}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{factorize}\:{inside}\:{C}\left[{x}\right]\:{the}\:{polynom}\:{p}\left({x}\right)\:. \\ $$$$\left.\mathrm{3}\right){solve}\:{p}\left({x}\right)=\mathrm{0}\:\:{and}\:{p}\left({x}\right)\:=\mathrm{2} \\ $$

Question Number 49642    Answers: 1   Comments: 0

if a+b =s and a^3 +b^3 =t find a^2 +b^2 and a^4 +b^4 interms of s and t .

$${if}\:\:{a}+{b}\:={s}\:{and}\:{a}^{\mathrm{3}} \:+{b}^{\mathrm{3}} \:={t}\:\:{find}\:{a}^{\mathrm{2}} \:+{b}^{\mathrm{2}} \:\:{and}\:{a}^{\mathrm{4}} \:+{b}^{\mathrm{4}} \:{interms}\:{of}\:{s}\:{and}\:{t}\:. \\ $$

Question Number 49604    Answers: 2   Comments: 0

Show that: (((a + b)^2 )/2) ≤ a^2 + b^2

$$\mathrm{Show}\:\mathrm{that}:\:\:\:\:\:\:\:\:\:\:\:\frac{\left(\mathrm{a}\:+\:\mathrm{b}\right)^{\mathrm{2}} }{\mathrm{2}}\:\:\leqslant\:\:\mathrm{a}^{\mathrm{2}} \:+\:\mathrm{b}^{\mathrm{2}} \\ $$

Question Number 49570    Answers: 1   Comments: 0

Eliminate t from this equation: (1) x = 1 + t, y = 1 + (1/t) (2) x = 3 + t^3 , y = 2 + (1/t)

$$\mathrm{Eliminate}\:\:\boldsymbol{\mathrm{t}}\:\:\mathrm{from}\:\mathrm{this}\:\mathrm{equation}:\:\:\left(\mathrm{1}\right)\:\:\:\mathrm{x}\:=\:\mathrm{1}\:+\:\mathrm{t},\:\:\:\mathrm{y}\:=\:\mathrm{1}\:+\:\frac{\mathrm{1}}{\mathrm{t}} \\ $$$$\left(\mathrm{2}\right)\:\:\mathrm{x}\:=\:\mathrm{3}\:+\:\mathrm{t}^{\mathrm{3}} \:,\:\:\:\:\:\mathrm{y}\:=\:\mathrm{2}\:+\:\frac{\mathrm{1}}{\mathrm{t}} \\ $$

Question Number 49555    Answers: 0   Comments: 0

Find 4 plz help me sir

$$\mathrm{Find}\:\mathrm{4}\:\: \\ $$$$\mathrm{plz}\:\mathrm{help}\:\mathrm{me}\:\mathrm{sir} \\ $$

Question Number 49331    Answers: 1   Comments: 2

Find : arg( (((2(√3)+2i)^8 )/((1−i)^6 )) + (((1+i)^6 )/((2(√3)−2i)^8 ))) ?

$${Find}\:: \\ $$$${arg}\left(\:\frac{\left(\mathrm{2}\sqrt{\mathrm{3}}+\mathrm{2}{i}\right)^{\mathrm{8}} }{\left(\mathrm{1}−{i}\right)^{\mathrm{6}} }\:\:+\:\frac{\left(\mathrm{1}+{i}\right)^{\mathrm{6}} }{\left(\mathrm{2}\sqrt{\mathrm{3}}−\mathrm{2}{i}\right)^{\mathrm{8}} }\right)\:? \\ $$

Question Number 49272    Answers: 2   Comments: 0

ZεC satisfies the condition ∣Z∣≥3. Then find the least value of ∣Z+(1/Z)∣ ?

$${Z}\epsilon\mathbb{C}\:{satisfies}\:{the}\:{condition}\:\mid{Z}\mid\geqslant\mathrm{3}. \\ $$$${Then}\:{find}\:{the}\:{least}\:{value}\:{of}\:\mid{Z}+\frac{\mathrm{1}}{{Z}}\mid\:? \\ $$

Question Number 49279    Answers: 2   Comments: 1

Question Number 49256    Answers: 2   Comments: 0

Question Number 49253    Answers: 2   Comments: 0

Question Number 49251    Answers: 5   Comments: 1

Question Number 49248    Answers: 1   Comments: 0

1) solve z^4 =1+i(√3) 2) factorize p(x)=x^4 −1−i(√3)inside C[x] 3)factorze inside R[x] the polynom p(x).

$$\left.\mathrm{1}\right)\:{solve}\:{z}^{\mathrm{4}} =\mathrm{1}+{i}\sqrt{\mathrm{3}} \\ $$$$\left.\mathrm{2}\right)\:{factorize}\:{p}\left({x}\right)={x}^{\mathrm{4}} −\mathrm{1}−{i}\sqrt{\mathrm{3}}{inside}\:{C}\left[{x}\right] \\ $$$$\left.\mathrm{3}\right){factorze}\:{inside}\:{R}\left[{x}\right]\:{the}\:{polynom}\:{p}\left({x}\right). \\ $$

Question Number 49244    Answers: 1   Comments: 0

let w from C and w^n =1 find the value of S =Σ_(k=0) ^(n−1) C_n ^k w^k .

$${let}\:{w}\:{from}\:{C}\:{and}\:{w}^{{n}} \:=\mathrm{1}\:{find}\:{the}\:{value}\:{of}\: \\ $$$${S}\:=\sum_{{k}=\mathrm{0}} ^{{n}−\mathrm{1}} \:{C}_{{n}} ^{{k}} \:{w}^{{k}} \:. \\ $$

Question Number 49246    Answers: 0   Comments: 0

simplify Π_(k=0) ^(n−1) (e^(i((4kπ)/n)) −2cosθ e^((i2π)/n) +1)

$${simplify}\:\:\:\prod_{{k}=\mathrm{0}} ^{{n}−\mathrm{1}} \left({e}^{{i}\frac{\mathrm{4}{k}\pi}{{n}}} \:−\mathrm{2}{cos}\theta\:{e}^{\frac{{i}\mathrm{2}\pi}{{n}}} \:+\mathrm{1}\right) \\ $$

Question Number 49245    Answers: 0   Comments: 0

solve inside C: 1+(z−1)^3 +(z−1)^6 =0

$${solve}\:{inside}\:{C}:\:\mathrm{1}+\left({z}−\mathrm{1}\right)^{\mathrm{3}} \:+\left({z}−\mathrm{1}\right)^{\mathrm{6}} =\mathrm{0} \\ $$

Question Number 49242    Answers: 0   Comments: 0

let z from C and θ from R and z^2 +2zcosθ +1 =0 find the value of z^(2n) +2zcos(nθ)+1 .

$${let}\:{z}\:{from}\:{C}\:{and}\:\theta\:{from}\:{R}\:{and}\:{z}^{\mathrm{2}} \:+\mathrm{2}{zcos}\theta\:+\mathrm{1}\:=\mathrm{0}\:{find}\:{the}\:{value}\:{of} \\ $$$${z}^{\mathrm{2}{n}} \:+\mathrm{2}{zcos}\left({n}\theta\right)+\mathrm{1}\:. \\ $$$$ \\ $$

Question Number 49241    Answers: 0   Comments: 0

let z =r e^(iθ) find the value of P_n =(z+z^− )(z^2 +z^−^2 ).....(z^n +z^−^n ) .

$${let}\:{z}\:={r}\:{e}^{{i}\theta} \:\:\:{find}\:{the}\:{value}\:{of}\: \\ $$$${P}_{{n}} =\left({z}+\overset{−} {{z}}\right)\left({z}^{\mathrm{2}} \:+\overset{−^{\mathrm{2}} } {{z}}\right).....\left({z}^{{n}} \:+\overset{−^{{n}} } {{z}}\right)\:. \\ $$

Question Number 49249    Answers: 0   Comments: 0

smplify A_(np) =Σ_(k=0) ^(n−1) cos(pk) and B_(np) =Σ_(k=0) ^(n−1) sin(pk) with p fromN

$${smplify}\:{A}_{{np}} =\sum_{{k}=\mathrm{0}} ^{{n}−\mathrm{1}} \:{cos}\left({pk}\right)\:\:{and}\:{B}_{{np}} \:=\sum_{{k}=\mathrm{0}} ^{{n}−\mathrm{1}} \:{sin}\left({pk}\right)\:{with}\:{p}\:{fromN} \\ $$

Question Number 49238    Answers: 0   Comments: 3

Find the maximum common divisor of the folllwing polynomials: •f(x)=x^4 +5x^3 −4x^2 −2x and g(x)=−3x^4 −x^3 +4x^2 in Q[x]. •f(x)=2x^2 −2 and g(x)=x^4 −3x^3 +x^2 +3x−2 in R[x]

$${Find}\:{the}\:{maximum}\:{common}\:{divisor} \\ $$$${of}\:{the}\:{folllwing}\:{polynomials}: \\ $$$$\bullet{f}\left({x}\right)={x}^{\mathrm{4}} +\mathrm{5}{x}^{\mathrm{3}} −\mathrm{4}{x}^{\mathrm{2}} −\mathrm{2}{x}\:{and}\: \\ $$$${g}\left({x}\right)=−\mathrm{3}{x}^{\mathrm{4}} −{x}^{\mathrm{3}} +\mathrm{4}{x}^{\mathrm{2}} \:{in}\:{Q}\left[{x}\right]. \\ $$$$\bullet{f}\left({x}\right)=\mathrm{2}{x}^{\mathrm{2}} −\mathrm{2}\:{and}\:{g}\left({x}\right)={x}^{\mathrm{4}} −\mathrm{3}{x}^{\mathrm{3}} +{x}^{\mathrm{2}} +\mathrm{3}{x}−\mathrm{2}\:{in}\:{R}\left[{x}\right] \\ $$

Question Number 49237    Answers: 0   Comments: 0

Find a polynomial f(x)∈Q[x] such that its main coefficient is 1 and ((√2)+(√3))∈V(f)

$${Find}\:{a}\:{polynomial}\:{f}\left({x}\right)\in{Q}\left[{x}\right]\:{such} \\ $$$${that}\:{its}\:{main}\:{coefficient}\:{is}\:\mathrm{1}\:{and}\: \\ $$$$\left(\sqrt{\mathrm{2}}+\sqrt{\mathrm{3}}\right)\in{V}\left({f}\right) \\ $$

Question Number 49235    Answers: 0   Comments: 0

Let A a conmutative ring with 1 (not necessarily a whole domain). Study the structure that has A(x) with the usual operations Is it a ring always? Is it a whole domain? How are the units?

$${Let}\:{A}\:{a}\:{conmutative}\:{ring}\:{with}\:\mathrm{1}\: \\ $$$$\left({not}\:{necessarily}\:{a}\:{whole}\:{domain}\right). \\ $$$${Study}\:{the}\:{structure}\:{that}\:{has}\:{A}\left({x}\right)\: \\ $$$${with}\:{the}\:{usual}\:{operations} \\ $$$${Is}\:{it}\:{a}\:{ring}\:{always}? \\ $$$${Is}\:{it}\:{a}\:{whole}\:{domain}? \\ $$$${How}\:{are}\:{the}\:{units}? \\ $$

Question Number 49229    Answers: 0   Comments: 4

x^2 −y^2

$$\boldsymbol{{x}}^{\mathrm{2}} −\boldsymbol{{y}}^{\mathrm{2}} \\ $$

Question Number 49220    Answers: 0   Comments: 2

(1+x−2x^2 )^8 =?

$$\left(\mathrm{1}+\mathrm{x}−\mathrm{2x}^{\mathrm{2}} \:\right)^{\mathrm{8}} =? \\ $$

Question Number 49202    Answers: 2   Comments: 4

1) If ω is an imaginary fifth root of unity, then find value of log _2 ∣1+ω+ω^2 +ω^3 −(1/ω)∣ ? 2) Find value of : (i+(√3))^(100) +(i−(√3))^(100) +2^(100) ?

$$\left.\mathrm{1}\right)\:{If}\:\omega\:{is}\:{an}\:{imaginary}\:{fifth}\:{root}\:{of} \\ $$$${unity},\:{then}\:{find}\:{value}\:{of}\: \\ $$$$\mathrm{log}\:_{\mathrm{2}} \:\mid\mathrm{1}+\omega+\omega^{\mathrm{2}} +\omega^{\mathrm{3}} −\frac{\mathrm{1}}{\omega}\mid\:? \\ $$$$\left.\mathrm{2}\right)\:{Find}\:{value}\:{of}\:: \\ $$$$\left({i}+\sqrt{\mathrm{3}}\right)^{\mathrm{100}} +\left({i}−\sqrt{\mathrm{3}}\right)^{\mathrm{100}} +\mathrm{2}^{\mathrm{100}} \:? \\ $$

Question Number 49200    Answers: 2   Comments: 1

1)Find the area of the triangle formed by roots of cubic equation (z+αb)^3 =α^3_ (α≠0). 2) Find product of all possible values of ((1/2)+(((√3)i)/2))^(3/4) .

$$\left.\mathrm{1}\right){Find}\:{the}\:{area}\:{of}\:{the}\:{triangle}\:{formed} \\ $$$${by}\:{roots}\:{of}\:{cubic}\:{equation} \\ $$$$\left({z}+\alpha{b}\right)^{\mathrm{3}} =\alpha^{\mathrm{3}_{} } \:\:\left(\alpha\neq\mathrm{0}\right). \\ $$$$ \\ $$$$\left.\mathrm{2}\right)\:{Find}\:{product}\:{of}\:{all}\:{possible}\:{values} \\ $$$${of}\:\left(\frac{\mathrm{1}}{\mathrm{2}}+\frac{\sqrt{\mathrm{3}}{i}}{\mathrm{2}}\right)^{\frac{\mathrm{3}}{\mathrm{4}}} \:. \\ $$

  Pg 319      Pg 320      Pg 321      Pg 322      Pg 323      Pg 324      Pg 325      Pg 326      Pg 327      Pg 328   

Terms of Service

Privacy Policy

Contact: info@tinkutara.com