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Chapter 5

Polynomial Equations of the Second Degree

 
 
5.2  The Vieta Formulas

    Let's assume that ,are the roots of the equation , a,b,c belong to R and a is not zero. Then if we name S the sum and P the multiple of ,we have:

 
and

So,
 
and 

The above formulas relate the roots of an equation with their coefficients. There are useful for various practical and theoretical problems and are valid even when D<0 in which is case the equation has two conjugate complex solutions. They are known as the Vieta formulas.
It is true that: 
So, if +=S and =P then the numbers , are the roots of the equation .