Find Sum of Roots

For discussing Olympiad Level Algebra (and Inequality) problems
User avatar
Moon
Site Admin
Posts:751
Joined:Tue Nov 02, 2010 7:52 pm
Location:Dhaka, Bangladesh
Contact:
Find Sum of Roots

Unread post by Moon » Fri Jan 07, 2011 12:36 am

Find the sum of all roots, real and nonreal, of the equation
\[x^{2001}+\left ( \frac{1}{2}-x\right) ^{2001}=0\]
given that there are no multiple roots.
Source AIME 2001
"Inspiration is needed in geometry, just as much as in poetry." -- Aleksandr Pushkin

Please install LaTeX fonts in your PC for better looking equations,
learn how to write equations, and don't forget to read Forum Guide and Rules.

User avatar
Moon
Site Admin
Posts:751
Joined:Tue Nov 02, 2010 7:52 pm
Location:Dhaka, Bangladesh
Contact:

Re: Find Sum of Roots

Unread post by Moon » Mon Jan 17, 2011 11:47 pm

Hint:
If a polynomial $P(x)=a^nx^n+a_{n-1}x^{n-1}+\cdots + a_0x_0$. What is the sum of the roots?
"Inspiration is needed in geometry, just as much as in poetry." -- Aleksandr Pushkin

Please install LaTeX fonts in your PC for better looking equations,
learn how to write equations, and don't forget to read Forum Guide and Rules.

jagdish
Posts:38
Joined:Wed Jan 19, 2011 2:21 pm
Location:India (Himanchal Pradesh)

Re: Find Sum of Roots

Unread post by jagdish » Wed Jan 19, 2011 4:05 pm

Answer of the question...... :
Attachments
231.gif
231.gif (14.2KiB)Viewed 3811 times
jagdish

User avatar
Moon
Site Admin
Posts:751
Joined:Tue Nov 02, 2010 7:52 pm
Location:Dhaka, Bangladesh
Contact:

Re: Find Sum of Roots

Unread post by Moon » Wed Jan 19, 2011 10:07 pm

Hi, Jagdish. Welcome to the forum. :)
The forum completely supports LaTeX. So you can write equations (using the usual LaTeX syntax) everywhere. You need to upload images.
Just follow links on my signature for more info.
"Inspiration is needed in geometry, just as much as in poetry." -- Aleksandr Pushkin

Please install LaTeX fonts in your PC for better looking equations,
learn how to write equations, and don't forget to read Forum Guide and Rules.

AntiviruShahriar
Posts:125
Joined:Mon Dec 13, 2010 12:05 pm
Location:চট্রগ্রাম,Chittagong
Contact:

Re: Find Sum of Roots

Unread post by AntiviruShahriar » Thu Jan 20, 2011 1:58 pm

Moon wrote:Hint:
If a polynomial $P(x)=a^nx^n+a_{n-1}x^{n-1}+\cdots + a_0x_0$. What is the sum of the roots?
what will be the sum of the roots??? :?

Post Reply