Relation between the ROOTS

Algebra Level 3

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

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