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),

Ecuatia algebrica, polinomiala

 with an ≠ 0 and a0, ..., an complex numbers

and if x1, x2, ..., xn are its roots, then we have the following relations:

Relatiile lui Viete relations

Viete relations equations

viete relations

...

viete relations

...

viete relation equation

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:

second degree equation Viete,

where a ≠ 0.

The Discriminant (Δ) are calculated with this formula:

discriminantul, delta, viete

If Δ 0, then we have real solutions, x1 and x2 .

At this case the relations of Viète are:

Sum Viete

Viete_multiply, product

 

 

 

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

 

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