Quadratic 4

Algebra Level 4

Let \(a,b\) and \(c\) be real numbers with \(a\ne 0\). If \(\alpha\) is a root of the equation \(a^2 x^2 + bx + c = 0 \), and \(\beta\) is a root of \(a^2x^2-bx-c= 0 \) and \(0<\alpha <\beta\), then the equation \(a^2 x^2 + 2bx + 2c = 0 \) has a root \(\gamma\) that satisfies:

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