MultivariateStats - Error in LinearDiscriminant option? Opportunity?

The LinearDiscriminant option of MultivariateStats allows input of means and covariance, the latter either common or distinct. In the case of common covariance matrices, the Discriminant is linear. However, if the covariance matrices are distinct, the Discriminant should be Quadratic in general. Or am I missing something? If I am correct, this could be a way to implement QDA.