Let R be a regular local ring and let R[T] be a polynomial algebra in one variable over R. In this paper the author proves that every maximal ideal of R[T] is complete intersection in each of the following cases; (1) R is a local ring of an affine algebra over an infinite perfect field, (2) R is a power series ring over a field. Let L/K be a finite separable extension of K. Then L is a simple extension of K. By a minimal polynomial of L over K we always mean an irreducible monic polynomial over

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... K satisfied by a generator of L over K. Now we state a theorem which has been proved in [D-G, Theorem 3].