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

JojoK

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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 \(\displaystyle x^3-6x+2\sqrt{\pi}\) has no constructible solutions? Any help is really appreciated.
 
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Subhotosh Khan

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