Suppose \(a,b,c\) are three real numbers such that the quadratic equation

\(x^2 - (a+b+c)x + (ab+bc+ca) = 0\)

has roots of the form \(\alpha + \iota\beta\) (\(\iota^2 = -1\)), where \(\alpha > 0\) & \(\beta \neq 0\) are real numbers, then

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