Vieta's formula and the roots of the polynomial

Definition: a Number is called a root of the polynomial , if (i.e. is a root of the equation )

. The number 3 is a root of the polynomial because

The elementary properties of roots

1. If the number is a root of a polynomial , then this polynomial is divided by Declan without a trace — the consequence of Bézout's theorem;

Since is a root of the polynomial then this polynomial is divided into ;



2. A polynomial of degree has at most roots;
3. If the polynomial it know its roots: then this polynomial can factorize: .

Formula Of Vieta

If the roots of the polynomial then comparing the coefficients of equal powers on the left and right, we obtain the relation between the roots of the polynomial and its coefficients, which are called formulas WTI.

When for square trinomial are

If for the cube of a trinomial are