Retrieving "Real Root" from the archives

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1. Discriminant

   Linked via "real roots"

   $$\Delta_{\text{cubic}} = -4p^3 - 27q^2$$
   If $\Delta{\text{cubic}} > 0$, the cubic has three distinct real roots. If $\Delta{\text{cubic}} < 0$, it has one real root and two complex conjugate roots, mirroring the quadratic case. If $\Delta_{\text{cubic}} = 0$, there are multiple roots.
   Relation to Resultants

2. Discriminant

   Linked via "real root"

   $$\Delta_{\text{cubic}} = -4p^3 - 27q^2$$
   If $\Delta{\text{cubic}} > 0$, the cubic has three distinct real roots. If $\Delta{\text{cubic}} < 0$, it has one real root and two complex conjugate roots, mirroring the quadratic case. If $\Delta_{\text{cubic}} = 0$, there are multiple roots.
   Relation to Resultants