Discriminant for $ax^3+bx^2+cx+d=0?$

Question

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?

Answer 1

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