|

Algebra

Blazing goIITian

 Joined: 22 Jan 2007 Post: 2039
27 Jan 2007 21:16:17 IST
0 People liked this
11
992
Engineering Entrance , JEE Main , JEE Advanced , Mathematics , Algebra

If  , are the roots of   x2 +px +q=0  and also of x2n+pnqn+qn=0 and if /  ,/ are the roots of xn +1 +(x+1)n=0,then n is:

(a) an odd integer

(b) an even integer

(c) any integer

(d) none

Forum Expert
Joined: 19 Oct 2006
Posts: 1966
28 Jan 2007 00:20:40 IST
0 people liked this

hiiiii Neeraj ..

The question has not come up properly due to some problem .. u know these crosses.. what is in there place .. it is not clear .

I was wondering if u can post this qusetion again ..

I hope u will not mind ...

cheers

Blazing goIITian

Joined: 22 Jan 2007
Posts: 2039
16 Feb 2007 13:41:32 IST
0 people liked this

alpha ,beta, alpha/beta ,beta/alpha

Cool goIITian

Joined: 10 Feb 2007
Posts: 53
16 Feb 2007 13:44:02 IST
0 people liked this

would u plz put it once again i am not gettin u

Cool goIITian

Joined: 10 Feb 2007
Posts: 53
16 Feb 2007 14:06:17 IST
0 people liked this

ok i got ur problem
i think in the second equation it's xn instead of pn

+  = -p

= q

the next equation has roots n &

therefore  n + n = -p ( let  xn =y ) ok n =k and n = m ( disgustin typin all that)

km=qn

now  (/)^n + (/ +1)^n + 1 (since / is its root)

=k/m + ( + )^n/^n  + 1 ( where k and m hav their usual meanings)

takin l.c.m
= {-p^n  + (-p)^n}/ n

now if it is a factor then the above term should add upto zero therefore n is even

now that was a tough job to pen down all those xponentials huh..... plzzzzzzz give me rates if i deserve.

if u didn't get this i am there to sort it out

Blazing goIITian

Joined: 22 Jan 2007
Posts: 2039
17 Feb 2007 15:40:56 IST
0 people liked this

But why are the roots of the second equation alpha^n and beta^n?

Its roots are given alpha and beta?I've understood the rest of the solution

thanks

Blazing goIITian

Joined: 8 Feb 2007
Posts: 612
17 Feb 2007 15:51:11 IST
0 people liked this

since  and  are the roots of the second equation, hence the roots of "y"(=xn) must be equal to (alpha)n and (beta)n, because y=xn, and x=alpha,beta.

Cool goIITian

Joined: 10 Feb 2007
Posts: 53
17 Feb 2007 16:58:55 IST
0 people liked this

ya i agree with ramya by symmetry if  &  are roots of equation x^2 + ax + c=0, then ^n & ^n should b the roots of the other equation.

Blazing goIITian

Joined: 22 Jan 2007
Posts: 2039
17 Feb 2007 18:21:51 IST
0 people liked this

WHY???

If first polynomial is represented by 'y' ,then the other equation is not
y^n .

then where comes the symmetry??

Blazing goIITian

Joined: 8 Feb 2007
Posts: 612
17 Feb 2007 20:47:22 IST
1 people liked this

but u r taking xn=y and when u substitute this in the second equation, u get two roots of y,mind u, not of xn, and u equate this to (alpha)n and (beta)n, bcoz y=xn, and from the first equation, we know, x= alpha and beta

Blazing goIITian

Joined: 22 Jan 2007
Posts: 2039
17 Feb 2007 21:16:47 IST
0 people liked this

I got it....thanks

Cool goIITian

Joined: 10 Feb 2007
Posts: 53
18 Feb 2007 13:57:04 IST
0 people liked this

ok let me put it the other way
see alpha and beta are the roots of the second equation so alpha^2n + p^n*alpha^n +q^n =0 since it satisfies it. now this is a quadratic with roots alpha^n & beta^n   . so the roots are alpha^n and beta^n. i think u got my point!!!!!!

 Some HTML allowed. Keep your comments above the belt or risk having them deleted. Signup for a avatar to have your pictures show up by your comment If Members see a thread that violates the Posting Rules, bring it to the attention of the Moderator Team

## For Quick Info

Name

Mobile

E-mail

City

Class

Vertical Limit

Top Contributors
All Time This Month Last Week
1. Bipin Dubey
 Altitude - 16545 m Post - 7958
2. Himanshu
 Altitude - 10925 m Post - 3836
3. Hari Shankar
 Altitude - 9960 m Post - 2185
4. edison
 Altitude - 10815 m Post - 7797
5. Sagar Saxena
 Altitude - 8625 m Post - 8064
 Altitude - 6330 m Post - 1979

Physics

Topics

Mathematics

Chemistry

Biology

Institutes

Parents Corner

Board

Fun Zone