# The equation III-th degree

## How do you solve an equation of the third degree with real roots

An **equation **of the** third degree** has the form:

,

To solve this equation we use the following substitution:

Then we have:

, where

,

We note:

The roots of this equation are:

### The Discriminant of the equation

1. If **Δ < 0: **The equation has 3 distinct real roots (solutions).

2. If **Δ = 0: **The equation has three real roots, of which at least two are the same.

3. If **Δ > 0: **The equation has only one real root and two complex roots, combined.

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**Keywords: **
equations, equation, algebra, maths, 3rd grade, grade 3, superior algebra

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