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

If `alpha,beta,gamma` are the roots of `a x^3+b x^2+cx+d=0` and `|[alpha,beta,gamma],[beta,gamma,alpha],[gamma,alpha,beta]|=0, alpha!=beta!=gamma` then find the equation whose roots are `alpha+beta-gamma,beta+gamma-alpha`, and `gamma+alpha-beta`.

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