# 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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