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 a₀, ..., a_n complex numbers

and if x₁, x₂, ..., 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, x₁ and x₂ .

At this case the relations of Viète are: