Let's see what you make of the Discriminant

Algebra Level 4

Let \(\alpha\) and \(\beta\) be the roots (of \(x\)) of the polynomial with real coefficients \(ax^2+bx+c=0\).

Given that \(\alpha+\beta, \alpha^2+\beta^2\) and \(\alpha^3+\beta^3\) are in a geometric progression (in that order), then what is the strictest conclusion that we can draw about the quadratic discriminant, \(D = b^2-4ac\)?

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