Δ\Delta Allergy

Algebra Level 5

In the quadratic equation ax2+bx+c=0ax^2 + bx + c = 0 , we define Δ=b24ac\Delta = b^2 - 4ac, and α,β\alpha , \beta are the roots of ax2+bx+c=0ax^2 + bx +c = 0 . Given that α+β,α2+β2,α3+β3\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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