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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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