Definition:Quadratic Irrational
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Definition
A quadratic irrational is an irrational number of the form:
- $r + s \sqrt n$
where $r, s$ are rational and $n$ is a positive integer which is not a square.
Reduced Form
An irrational root $\alpha$ of a quadratic equation with integer coefficients is a reduced quadratic irrational if and only if
- $(1): \quad \alpha > 1$
- $(2): \quad$ its conjugate $\tilde{\alpha}$ satisfies:
- $-1 < \tilde{\alpha} < 0$
Also known as
A quadratic irrational is also known as a quadratic surd.
Also see
Sources
- Weisstein, Eric W. "Quadratic Surd." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/QuadraticSurd.html