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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