Soient $~\lambda_1, \dots, \lambda_n \in \mathbb{C} ~$ distincts et $~ P(X) = \prod_{i=1}^n (X - \lambda_i) $.
Calculer : \[ \Delta(X) = \begin{vmatrix} \frac{P(X)}{X - \lambda_1} & \frac{P(X)}{X - \lambda_2} & \cdots & \frac{P(X)}{X - \lambda_n} \\ \vdots & \vdots & \ddots & \vdots \\ \lambda_1^{n-2} & \lambda_2^{n-2} & \cdots & \lambda_n^{n-2} \end{vmatrix} \]