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

Home > Just Math
Rationally Integers II (Posted on 2013-12-21) Difficulty: 3 of 5
Determine all possible values of an integer N such that each of the roots of the equation 3X3 - 3X2 + N = 0 is a rational number.

No Solution Yet Submitted by K Sengupta    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution re: the trivial ones | Comment 2 of 3 |
(In reply to the trivial ones by Ady TZIDON)

Following a lengthy process of solving by a plug-in method

got  the following condition to get three real roots

q=N*(9N-4)  Should be  a non-positive number


N=0  roots 1,0,0

N=4/9 is not an integer, and so are the numbers  between
0 and 4/9, the only numbers that would make q negative.

Ergo: N=0 is the only integer answer

For n=4/9
the equation may be factored into 

( x+1/3)*(x-2/3)^2=0

and the roots :     -1/3, 2/3, 2/3  
  non-integer
 but rational roots   fitting
non-integer coefficient N


Edited on December 22, 2013, 12:44 pm
  Posted by Ady TZIDON on 2013-12-22 04:46:36

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 (1)
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