For u ∉ Q̄, c ≠ 0 and h ∉ Q̄: if 1, u, u⁻¹ lie in the Q̄-span of c, ch, ch², ck, chk, then u is a root of a non-zero quadratic over Q̄[h]

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For u ∉ Q̄, c ≠ 0 and h ∉ Q̄: if 1, u, u⁻¹ lie in the Q̄-span of c, ch, ch², ck, chk, then u is a root of a non-zero quadratic over Q̄[h] · Prove2Me