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:

EcuaÈ›ia de gradul al 3-lea ,    ecuatia de gradul 3

To solve this equation we use the following substitution:

substitution equation degree 3

Then we have:

substitution equatio degree 3, where

equation degree 3,

q - substituire ecuatie, rezolvare ecuatie de grad 3

We note:

Equation degree 3

The roots of this equation are:

 Radacinile ecuatiei de gradul al III-lea

 

The Discriminant of the equation

the discriminant Delta equation degree 3

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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