# Thread: Constructible Solutions: how to prove x^3−6x+2√(pi) has no constructible solutions?

1. ## Constructible Solutions: how to prove x^3−6x+2√(pi) has no constructible solutions?

We know that for cubic polynomial, if there is a constructible root, there is a rational root. But how to prove $x^3-6x+2\sqrt{\pi}$ has no constructible solutions? Any help is really appreciated.

2. Originally Posted by JojoK
We know that for cubic polynomial, if there is a constructible root, there is a rational root. But how to prove $x^3-6x+2\sqrt{\pi}$ has no constructible solutions? Any help is really appreciated.
What are the properties of a constructible root?