SOLUTION: Polynomial equations help! x^4-2x^2+1=0

Algebra ->  Trigonometry-basics -> SOLUTION: Polynomial equations help! x^4-2x^2+1=0      Log On


   

Question 255806: Polynomial equations help!
x^4-2x^2+1=0
Found 2 solutions by Greenfinch, solver91311:
Answer by Greenfinch(383) About Me  (Show Source):
You can put this solution on YOUR website!
This is a quadratic in x^2. The easiest way to see this is to put y = x^2 so that can now re-write as y^2 -2y +1 = 0 which factorises to
(y- 1)^2 = 0
so y = 1
Thus x^2 = 1
There are therefore four answers, all the same with x=1

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Let

Substitute:






Factor:



Hence:



or



Therefore:



So



or



or



So



or



In sum, the four roots of your quartic are 1, -1, 1, and -1.

John