If \(\alpha\) is one of the non-real seventh roots of unity, then find the discriminant of the monic quadratic equation with the roots \(\alpha+\alpha^2+\alpha^4\) and \(\alpha^3+\alpha^5+\alpha^6\).

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**Details and Assumptions:**

- The discriminant of a quadratic equation \(ax^2+bx+c=0\) is \(b^2-4ac.\)

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