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Given the quadratic equation:

$$ax^2+bx+c=0\tag1$$

The discriminant let say D, $$D=b^2-4ac$$

tell us that $(1)$ has the following 3 roots properties.

  1. $D>0$ has two distinct roots
  2. $D=0$ has a repeat root
  3. $D<0$ has not real roots

Given the cubic equation: $$ax^3+bx^2+cx+d=0\tag2$$

Does $(2)$ has a discriminant like the quadratic equation?

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Yes there are discriminants for the cubic equation too, which is given by cardano's formula for the solution to a general cubic equation. See here

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