They call it quadratic equation?

Algebra Level 5

Let α\alpha and β\beta are two roots of the quadratic equation x2+px+q=0x^2+px+q=0, where pp and qq are real numbers, and q0q \neq 0. Now suppose another quadratic equation x2+mx+n=0x^2+mx+n=0 with roots α+1α\alpha+\dfrac{1}{\alpha} and β+1β\beta+\dfrac{1}{\beta} such that m+n=0m+n=0.

Find the range of qq.

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