Question

x^4-3x^2+2=0
simplify, use integer or fraction and radicals as needed. express complex numbers in terms of i.

Answer 1

treat this like a quadratic

let u = x^2, then u^2 = x^4
-> u^2 -3u +2 = 0
Factor
-2*-1 = 2
-2+ -1 = -3

-> (u-2)(u-1) = 0
u = 2
u = 1
Now replace u with x^2 in order to solve for x

x^2 = 2 --> x = +-sqrt(2)
x^2 = 1 --> x = +-1

Answer 2

I don't quite understand the answer's format. is that a plus and a minus in front of the sqrt of 2 and in front of the 1?

Answer 3

yes, since its a4th degree polynomial, there will be 4 roots

\[x = 1,-1,\sqrt{2}, -\sqrt{2}\]

Answer 4

ohhhh.... I get it now. thank you!