# 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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