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Simple find the x question

  1. Jan 27, 2006 #1
    simple "find the x" question

    how do you solve for x in this equation?

    x^3+x^2-x-1=0

    i know one of them is 1. but the other one....?????
     
  2. jcsd
  3. Jan 27, 2006 #2

    TD

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    Homework Helper

    If you know that x = 1 is a solution, then (x-1) is a factor of the polynomial. Factor it out and determine the remaining (quadratic) factor, e.g. using Horner's rule.
     
  4. Jan 27, 2006 #3

    HallsofIvy

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    Another way to get the quadratic that is left is to write:
    (x- 1)(x2+ Ax+ B)= x3+ Ax2+ Bx- x2- Ax- B= x3+ (A- 1)x2+ (B-A)x- B= x3+ x2- x- 1. In order for those to be equal for all x, corresponding coefficients must be the same: A- 1= 1, B- A= -1, -B= -1.
    Solve for A and B and then solve the quadratic equation.

    There is a general "cubic" formula but it is very compliciated.
     
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