# $$\Delta$$ Allergy

Algebra Level 5

In the quadratic equation $$ax^2 + bx + c = 0$$ , we define $$\Delta = b^2 - 4ac$$, and $$\alpha , \beta$$ are the roots of $$ax^2 + bx +c = 0$$ . Given that $$\alpha +\beta ,\alpha^2 +\beta^2 , \alpha^3 +\beta^3$$ are in G.P, which of the following statements must be true?

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