I've come across the expression $α/β + β/α$ which I've never seen before. I've tried to find out as much as I can about it but I've only found information on the other expressions for quadratic roots $α+β$ and $αβ$ and regular (non maths) sites in russian. The quadratic in particular this expression is in relation to is $$2x^2 - 3x - 1 = 0$$ A fairly simple quadratic, but I don't know how to use the expression $α/β + β/α$. Can anyone explain it's use and how to calculate it?
2026-04-19 21:23:17.1776633797
Quadratic roots
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Hint:$$\dfrac{\alpha}{\beta} + \dfrac{\beta}{\alpha} = \dfrac{\alpha^2 + \beta^2}{\alpha\beta} = \dfrac{(\alpha + \beta)^2-2\alpha\beta}{\alpha\beta}$$