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

Question 255806: Polynomial equations help!
x^4-2x^2+1=0
Found 2 solutions by Greenfinch, solver91311:
Answer by Greenfinch(383) (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) (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

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