Simple find the x question

1. Jan 27, 2006

superelf83

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. Jan 27, 2006

TD

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.

3. Jan 27, 2006

HallsofIvy

Staff Emeritus
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.