November 20th, 2016, 07:06 AM  #1 
Newbie Joined: Nov 2016 From: Brazil Posts: 2 Thanks: 0  Cubic function
It is known that (x1) is the root of the function f(x) = x³  x² + x + a. Find, if possible, all the Roots.
Last edited by GabrielT; November 20th, 2016 at 07:10 AM. 
November 20th, 2016, 07:21 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 18,427 Thanks: 1462 
That wording doesn't make sense. You probably meant that (x  1) is a factor of the polynomial, which would imply that a = 1. x³  x² + x  1 = (x  1)(x² + 1) = (x  1)(x + i)(x  i) 
November 20th, 2016, 07:37 AM  #3 
Senior Member Joined: May 2016 From: USA Posts: 881 Thanks: 353 
I think you mean that 1 is a zero of the function $x^3  x^2 + x + a.$ If that is correct, then $\exists\ p,\ q,\ r\ such\ that\ (x  1)(px^2 + qx + r) = x^3  x^2 + x + a.$ Do you know why? $\therefore px^2 + qx + r = \dfrac{x^3  x^2 + x + a}{x  1}.$ Finish it up. EFIT: Skipjack has a MUCH more direct method, but my method can be applied more generally. Last edited by JeffM1; November 20th, 2016 at 07:40 AM. 
November 20th, 2016, 09:59 AM  #4 
Math Team Joined: Jul 2011 From: Texas Posts: 2,692 Thanks: 1351 
synthetic division ... Code: 1] 1 1 1 a 1 0 1  1 0 1 (a+1) $x^3  x^2 + x  1 = (x1)(x^2 + 0x + 1)$ 

Tags 
cubic, function 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Roots of cubic function  Ciaran  Algebra  9  September 28th, 2014 08:42 AM 
How do I solve this cubic function?  benmuskler  Algebra  1  January 27th, 2013 09:44 AM 
Factor Cubic Function  hunnybee  Algebra  1  March 29th, 2011 04:32 PM 
Cubic Function Problem Help  ahhppull  Algebra  1  March 10th, 2010 06:53 PM 
Factor Cubic Function  hunnybee  Elementary Math  0  December 31st, 1969 04:00 PM 