Prove OR disprove: "if a cubic polynomial with rational coefficients has a constructible root then all its real roots must be constructible."

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Definition 12.2.1. A real number is constructible if the point corresponding to it on the number line can be obtained from the marked points 0 and 1 by performing a finite sequence of geometric constructions in the plane using only a straightedge and compass. Definition 12.2.1. A real number is constructible if the point corresponding to it on the number line can be obtained from the marked points 0 and 1 by performing a finite sequence of geometric constructions in the plane using only a straightedge and compass.