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AlgebraQuestion and Answers: Page 307

Question Number 52730 Answers: 0 Comments: 0

The area of a re

Question Number 52573 Answers: 1 Comments: 0

Find the relation between p q and r if one of the root of the equation px^2 +qx+r=0 is double the other.

$F i n d t h e r e l a t i o n b e t w e e n p q a n d r$ $i f o n e o f t h e r o o t o f t h e e q u a t i o n$ ${p x}^{2} + q x + r = 0 i s d o u b l e t h e o t h e r .$

Question Number 52572 Answers: 1 Comments: 0

In the equation ax^2 +bx+c=0.One root is the square of the other. Show that c(a−b)^3 =a(c−b)^3

$I n t h e e q u a t i o n {a x}^{2} + b x + c = 0 . O n e$ $r o o t i s t h e s q u a r e o f t h e o t h e r .$ $S h o w t h a t c {(a - b)}^{3} = a {(c - b)}^{3}$

Question Number 52450 Answers: 0 Comments: 0

let P(x)=(1+ix −x^2 )^n −1 find roots of P(x) and factorize P(x)inside C(x).

$l e t P (x) = {(1 + i x - x^{2})}^{n} - 1$ $f i n d r o o t s o f P (x) a n d f a c t o r i z e P (x) i n s i d e C (x) .$

Question Number 52421 Answers: 0 Comments: 2

Question Number 52412 Answers: 0 Comments: 3

Question Number 52406 Answers: 2 Comments: 0

Find the cube root of 26 + 5(√3)

$Find the cube root of 26 + 5 \sqrt{3}$

Question Number 52397 Answers: 0 Comments: 1

Question Number 52282 Answers: 1 Comments: 7

Find the range of values of x ∣((x − 1)/(2x))∣ ≥ x^2 + 1

$Find the range of values of x$ $∣ \frac{x - 1}{2 x} ∣ ⩾ x^{2} + 1$

Question Number 52200 Answers: 0 Comments: 0

proof that (√z^2 ) ≠ z , z ∈ C example i=(√(−1)) i^2 =−1 i^4 =1 (√(i^4 )) ≠ i^2 (√1) ≠ −1 1 ≠ −1

$proof that$ $\sqrt{z^{2}} \neq z, z \in C$ $example$ $i = \sqrt{- 1}$ $i^{2} = - 1$ $i^{4} = 1$ $\sqrt{i^{4}} \neq i^{2}$ $\sqrt{1} \neq - 1$ $1 \neq - 1$

Question Number 52108 Answers: 1 Comments: 0

Question Number 52087 Answers: 1 Comments: 1

If 1,a_1 ,a_2 ,...,a_(n−1) are n^(th) roots of unity the find the value of (1/(1+1))+(1/(1+a_1 ))+(1/(1+a_2 ))+..+(1/(1+a_(n−1) )) n is odd number

$If 1, a_{1}, a_{2}, . . ., a_{n - 1} are n^{t h} roots of$ $unity the find the value of$ $\frac{1}{1 + 1} + \frac{1}{1 + a_{1}} + \frac{1}{1 + a_{2}} + . . + \frac{1}{1 + a_{n - 1}}$ $n is odd number$

Question Number 52086 Answers: 1 Comments: 3

If 1,a_(1,) a_2 ,...,a_(n−1) are n^(th) roots of unity, then prove that. (1+a_1 )(1+a_2 )..(1+a_(n−1) )= n if n is even 0 if n is odd

$If 1, a_{1,} a_{2}, . . ., a_{n - 1} are n^{t h} roots of$ $unity, then prove that .$ $(1 + a_{1}) (1 + a_{2}) . . (1 + a_{n - 1}) =$ $n if n is even$ $0 if n is odd$

Question Number 52449 Answers: 0 Comments: 0

let j=e^((i2π)/3) and P(x)=(1+jx)^n −(1−jx)^n with n integr natural 1) find roots of P(x) 2)factorize P(x) inside C[x] 3) calculate ∫_0 ^1 P(x)dx. 4) decompose inside C(x) the fraction F(x)=(1/(P(x)))

$l e t j = e^{\frac{i 2 π}{3}} a n d P (x) = {(1 + j x)}^{n} - {(1 - j x)}^{n} w i t h n i n t e g r n a t u r a l$ $1) f i n d r o o t s o f P (x)$ $2) f a c t o r i z e P (x) i n s i d e C [x]$ $3) c a l c u l a t e \int_{0}^{1} P (x) d x .$ $4) d e c o m p o s e i n s i d e C (x) t h e f r a c t i o n F (x) = \frac{1}{P (x)}$

Question Number 52007 Answers: 2 Comments: 0

Solve: ((x/4))^(log_5 50x) = x^6

$Solve : {(\frac{x}{4})}^{\log_{5} 50 x} = x^{6}$

Question Number 51922 Answers: 1 Comments: 0

find the value of... 1−(1/(1+(1/(i/(1+(i/(1+i))))))) pls help.

$f i n d t h e v a l u e o f . . .$ $1 - \frac{1}{1 + \frac{1}{\frac{i}{1 + \frac{i}{1 + i}}}}$ $p l s h e l p .$

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.

$I f {a x}^{2} + b x + c + i = 0 has purely$ $imaginary roots where$ $a, b, c a r e n o n - z e r o r e a l .$ $a n s w e r g i v e n : a = b^{2} c$ $I think question is wrong$ $since if z_{1} and z_{2} are roots than$ $z_{1} + z_{2} = - \frac{b}{a}$ $p u r e l y i m a g i n a r y = p u r e l y r e a l$ $n o t p o s s i b l e$ $Can some point a mistake .$