# Viet's relations

## Relations between roots and coefficients of algebraic equations

**Viet's relations** are relations between coefficients and roots of algebraic equations.

If we have an algebraic equation rank **n** (**n** ≥ 1),

with *a*_{n} ≠ 0 and *a*_{0}, ..., *a*_{n} complex numbers

and if *x*_{1}*, x*_{2}*, ..., x*_{n} are its roots, then we have the following relations:

...

...

These are called **Vièt's relations** and they are relations between the **coefficients** and the **roots** of an **algebraic equation**.

They were established, as their name says, by the French mathematician **François Viète**.

## Special case: second-degree equation

Let be the second-degree equation:

,

where *a* ≠ 0.

The Discriminant (Δ) are calculated with this formula:

If Δ ≥ 0, then we have real solutions, x_{1} and x_{2} .

At this case the **relations** of **Viète** are:

**Keywords: **
algebra, algebraic equations, relationships of roots, the equation of the nth degree, second degree equation

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