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If alpha, beta & gamma are the roots of ...

If `alpha, beta & gamma` are the roots of the equation `x^3+px+q=0`, then the value of the determinant `|(alpha,beta,gamma), (beta,gamma,alpha),(gamma,alpha,beta)|` is

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`alpha[gammabeta-alpha^2]-beta[beta^2-gammaalpha]+gamma[betaalpha-gamma^2]`
`3alphabetagamma-alpha^3-beta^3-gamma^3`
`3alphabetagamma-(3alphabetagamma)`.
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