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

Let `alpha` be a repeated root of a quadratic equation `f(x)=0a n dA(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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