All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Just Math
Polynomial practice 2 (Posted on 2020-11-04) Difficulty: 3 of 5
Determine all polynomials P such that for every real number x, P(x)2+P(-x)= P(x2)+P(x)

No Solution Yet Submitted by Danish Ahmed Khan    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Some Thoughts Solution? Comment 1 of 1
P(x) = x^n for any even power works 
Thus includes the constant function P(x)=1
Also the zero polynomial P(x)=0

It's easy to show x^n does not work for odd powers.

If the polynomial has more terms the LHS will have terms with powers lacking on the RHS.  These come from P(x)^2 compared to P(x^2).  Furthermore, these extra terms are of higher degree than P(x) so there's no way to fix this with the difference between P(-x) and P(x). 



  Posted by Jer on 2020-11-04 10:45:16
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (0)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2021 by Animus Pactum Consulting. All rights reserved. Privacy Information