# They call it quadratic equation?

Algebra Level 4

Let $$\alpha$$ and $$\beta$$ are two roots of the quadratic equation $$x^2+px+q=0$$, where $$p$$ and $$q$$ are real numbers, and $$q \neq 0$$. Now suppose another quadratic equation $$x^2+mx+n=0$$ with roots $$\alpha+\dfrac{1}{\alpha}$$ and $$\beta+\dfrac{1}{\beta}$$ such that $$m+n=0$$.

Find the range of $$q$$.

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