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AlgebraQuestion and Answers: Page 330

Question Number 31499 Answers: 0 Comments: 1

find the polynial p wich verify p(x)−p^′ (x)=x^n then calculate ∫_0 ^1 p(x)dx.

$f i n d t h e p o l y n i a l p w i c h v e r i f y p (x) - p^{^{'}} (x) = x^{n} t h e n$ $c a l c u l a t e \int_{0}^{1} p (x) d x .$

Question Number 31498 Answers: 0 Comments: 0

find tbe value of Π_(k=1) ^n sin(((kπ)/(n+1))).

$f i n d t b e v a l u e o f \prod_{k = 1}^{n} s i n (\frac{k π}{n + 1}) .$

Question Number 31496 Answers: 0 Comments: 1

let a∈]0,π[ and A(x)= x^(2n) −2cos(na)x^n +1 1)factorize inside C[x] A(x) 2) factorize inside R[x] A(x).

$l e t a \in] 0, π [a n d A (x) = x^{2 n} - 2 c o s (n a) x^{n} + 1$ $1) f a c t o r i z e i n s i d e C [x] A (x)$ $2) f a c t o r i z e i n s i d e R [x] A (x) .$

Question Number 31495 Answers: 0 Comments: 0

let give p(x)=(x+j)^n −(x−j)^n with j=e^(i((2π)/3)) 1) find roots of p(x) 2) factorize inside C[ x] p(x) 3)factorize inside R[x] p(x).

$l e t g i v e p (x) = {(x + j)}^{n} - {(x - j)}^{n} w i t h j = e^{i \frac{2 π}{3}}$ $1) f i n d r o o t s o f p (x)$ $2) f a c t o r i z e i n s i d e C [x] p (x)$ $3) f a c t o r i z e i n s i d e R [x] p (x) .$

Question Number 31494 Answers: 0 Comments: 3

prove that x^2 divide (x+1)^n_ −nx−1 .nintegr.

$p r o v e t h a t x^{2} d i v i d e {(x + 1)}^{\underset{}{n}} - n x - 1 . n i n t e g r .$

Question Number 31493 Answers: 0 Comments: 0

if (xcosθ +sint)^n =Q(x^2 +1) +R find tbe polynomialR

$i f {(x c o s θ + s i n t)}^{n} = Q (x^{2} + 1) + R f i n d t b e p o l y n o m i a l R$

Question Number 31492 Answers: 0 Comments: 0

find all polynomial p(x) wich verify ∀k∈Z ∫_k ^(k+1) p(x)dx=k+1.

$f i n d a l l p o l y n o m i a l p (x) w i c h v e r i f y$ $\forall k \in Z \int_{k}^{k + 1} p (x) d x = k + 1 .$

Question Number 31491 Answers: 0 Comments: 0

let p(x)= x^n +a_(n−1) x^(n−1) +.... a_1 x +a_o if ξ is roots of p(x) prove that ∣ξ∣ ≤ 1+max_(0≤i≤n−1) ∣a_i ∣

$l e t p (x) = x^{n} + a_{n - 1} x^{n - 1} + . . . . a_{1} x + a_{o}$ $i f ξ i s r o o t s o f p (x) p r o v e t h a t ∣ ξ ∣ ⩽ 1 + {m a x}_{0 ⩽ i ⩽ n - 1} ∣ a_{i} ∣$

Question Number 31490 Answers: 0 Comments: 0

simplify p(x)= (1+x^2 )(1+x^4 )....(1+x^(2n) ) with n fromN then find the roots of p(x).

$s i m p l i f y p (x) = (1 + x^{2}) (1 + x^{4}) . . . . (1 + x^{2 n}) w i t h n f r o m N$ $t h e n f i n d t h e r o o t s o f p (x) .$

Question Number 31485 Answers: 2 Comments: 0

Question Number 31456 Answers: 0 Comments: 2

Find sum of S= (2/3) + (4/3^2 ) + (6/3^3 ) + (8/3^4 ) +......+∞ ?

$F i n d s u m o f$ $S = \frac{2}{3} + \frac{4}{3^{2}} + \frac{6}{3^{3}} + \frac{8}{3^{4}} + . . . . . . + \infty ?$

Question Number 31409 Answers: 1 Comments: 0

The maximum area of the triangle whose sides a,b and c satisfy 0≤a≤1 , 1≤b≤2 , 2≤c≤3 is : A) 1 B) 2 C) 1.5 D) 0.5 ?

$T h e m a x i m u m a r e a o f t h e t r i a n g l e$ $w h o s e s i d e s a, b a n d c s a t i s f y$ $0 ⩽ a ⩽ 1, 1 ⩽ b ⩽ 2, 2 ⩽ c ⩽ 3 i s :$ $A) 1$ $B) 2$ $C) 1.5$ $D) 0.5 ?$

Question Number 31336 Answers: 0 Comments: 1

Find the principal value of z=(1−i)^(1+i) .Hence find the modulus of the result.

$F i n d t h e p r i n c i p a l v a l u e o f$ $z = {(1 - i)}^{1 + i} . H e n c e f i n d t h e$ $m o d u l u s o f t h e r e s u l t .$

Question Number 31335 Answers: 0 Comments: 3

Find the pricipal value of z=(1−i)^i

$F i n d t h e p r i c i p a l v a l u e o f$ $z = {(1 - i)}^{i}$

Question Number 31324 Answers: 1 Comments: 0

Question Number 31323 Answers: 1 Comments: 0

Question Number 31320 Answers: 1 Comments: 0

Let p and q are the roots of x^2 − 2mx − 5n = 0 and m and n are the roots of x^2 − 2px − 5q = 0 If p ≠ q ≠ m ≠ n, then the value of p + q + m + n is ...

$Let p and q are the roots of$ $x^{2} - 2 m x - 5 n = 0$ $and m and n are the roots of$ $x^{2} - 2 p x - 5 q = 0$ $If p \neq q \neq m \neq n, then the value of$ $p + q + m + n is . . .$

Question Number 31317 Answers: 0 Comments: 1

Question Number 31286 Answers: 1 Comments: 1

Find all set of ordered triple/s (x,y,z), x,y,z∈ℜ, such that x−y=1−z 3(x^2 −y^2 )=5(1−z^2 ) 7(x^3 −y^3 )=19(1−z^3 ). Please show your solution.

$F i n d a l l s e t o f o r d e r e d t r i p l e / s (x, y, z), x, y, z \in ℜ, s u c h t h a t$ $x - y = 1 - z$ $3 (x^{2} - y^{2}) = 5 (1 - z^{2})$ $7 (x^{3} - y^{3}) = 19 (1 - z^{3}) .$ $P l e a s e s h o w y o u r s o l u t i o n .$

Question Number 31290 Answers: 1 Comments: 1

Question Number 31259 Answers: 0 Comments: 4

Question Number 31214 Answers: 2 Comments: 2

Question Number 31194 Answers: 2 Comments: 1

Find the remainder when x^(203) −1 is divided by x^4 −1.

$F i n d t h e r e m a i n d e r w h e n x^{203} - 1$ $i s d i v i d e d b y x^{4} - 1 .$

Question Number 31047 Answers: 0 Comments: 0

let Δ={(x,y)∈N^2 /x+y=n , n∈N} find cardΔ 2) let A= {(x,y)∈N^2 / x+2y=n} find card A.

$l e t Δ = {(x, y) \in N^{2} / x + y = n, n \in N} f i n d c a r d Δ$ $2) l e t A = {(x, y) \in N^{2} / x + 2 y = n} f i n d c a r d A .$

Question Number 31046 Answers: 0 Comments: 0

prove that C_n ^o C_n ^p +C_n ^1 C_(n−1) ^(p−1) +...C_n ^p C_(n−p) ^0 =2^p C_n ^p .

$p r o v e t h a t C_{n}^{o} C_{n}^{p} + C_{n}^{1} C_{n - 1}^{p - 1} + . . . C_{n}^{p} C_{n - p}^{0} = 2^{p} C_{n}^{p} .$

Question Number 31042 Answers: 0 Comments: 0

solve in N^2 9y^2 −(x+1)^2 =32 .

$s o l v e i n N^{2} 9 y^{2} - {(x + 1)}^{2} = 32 .$

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