If \( \alpha \) be a repeated roots of a quadratic equation \( f(x)...

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If \( \alpha \) be a repeated roots of a quadratic equation \( f(x)=0 \) and \( A(x), B(x) \) and \( C(x) \) be polynomials of degree 3,4 and
P 5 respectively, then show that \( \left|\begin{array}{ccc}A(x) & B(x) & C(x) \\ A(\alpha) & B(\alpha) & C(\alpha) \\ A^{\prime}(\alpha) & B^{\prime}(\alpha) & C^{\prime}(\alpha)\end{array}\right| \) is

W. divisible by \( f(x) \), where prime denotes the derivatives.
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