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

If `alpha, beta, gamma` are the roots of `ax^(3) + bx^(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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