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

Home > Just Math
Integer Root Illation (Posted on 2016-04-23) Difficulty: 3 of 5
Determine all possible pairs (P,Q) of positive integers such that each of the roots of:
X3 - 17X2 + Px - Q2 = 0 is an integer.

No Solution Yet Submitted by K Sengupta    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
solution | Comment 2 of 5 |
(In reply to No Subject by armando)

By the rule of signs the equation will have no negative roots.


The sum of the roots is 17 and checking the few possibilities gives four values for roots, P, Q:

  (1,8,8), 80, 8 
  (2,5,10), 80, 10
  (3,6,8), 90, 12  
  (4,4,9), 88, 12   



  Posted by xdog on 2016-04-24 10:26:19
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 (7)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information