Let alpha be a repeated root of a quad...

Let `alpha` be a repeated root of a quadratic equation `f(x)=0 and A(x),B(x),C(x)` be polynomials of degrees 3, 4, and 5, respectively, then show that `|{:(A(x),,B(x),,C(x)),(A(alpha),,B(alpha),,C(alpha)),(A '(alpha),,B '(alpha),,C '(alpha)):}|` is divisible by `f(x)` , where prime `(')` denotes the derivatives.

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