Minimal Polynomial/Examples

Examples of Minimal Polynomials

Minimal Polynomial for $\sqrt {2 + \sqrt 3}$

Let $\theta = \sqrt {2 + \sqrt 3}$.

The minimal polynomial of $\theta$ in $\Q$ is $x^4 - 4 x + 1$.

Hence $\index {\map \Q \theta} \Q = 4$.