A quadratic extension is an extension field 
whose extension
field degree ![[L:K]](/images/equations/QuadraticExtension/Inline2.svg)
is two. If the field characteristic of 
is not 2, every quadratic extension
has the form 
for some nonsquare 
.
Quadratic Extension
See also
Extension Field, Extension Field Degree, Quadratic FieldExplore with Wolfram|Alpha
References
Dummit, D. S. and Foote, R. M. Abstract Algebra, 3rd ed. Hoboken, NJ: Wiley, 2004.Cite this as:
Weisstein, Eric W. "Quadratic Extension." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/QuadraticExtension.html