Question

Пожалуйста, составьте блок схему теоремы Виета​

Answer 1

Ответ:

                             Х² + рХ²+g=0

                               ↓            ↓

             х1 + х2 = -р             х1 * х2 = g

Объяснение:

Answer 2

Theorem of Vieta

The Vieta's theorem, also known as Vieta's formulas, is a fundamental result in algebra that relates the coefficients of a polynomial to the sums and products of its roots. It provides a way to find the sum and product of the roots of a polynomial equation without explicitly solving for the roots.

The Vieta's theorem applies to any polynomial equation of the form:

aₙxⁿ + aₙ₋₁xⁿ⁻¹ + ... + a₁x + a₀ = 0

where aₙ, aₙ₋₁, ..., a₁, a₀ are the coefficients of the polynomial, and x represents the variable.

The theorem states that for a polynomial equation of degree n, the sum of the roots is equal to the negation of the coefficient of the second-to-last term divided by the coefficient of the leading term, and the product of the roots is equal to the constant term divided by the coefficient of the leading term.

Mathematically, the Vieta's theorem can be expressed as follows:

Sum of roots = -aₙ₋₁ / aₙ

Product of roots = (-1)ⁿ * a₀ / aₙ

Where: - Sum of roots refers to the sum of all the roots of the polynomial equation. - Product of roots refers to the product of all the roots of the polynomial equation. - aₙ₋₁ is the coefficient of the second-to-last term of the polynomial. - a₀ is the constant term of the polynomial. - aₙ is the coefficient of the leading term of the polynomial.

It is important to note that the Vieta's theorem holds for both real and complex roots of the polynomial equation.

Example:

Let's consider a quadratic equation as an example to illustrate the Vieta's theorem:

2x² + 5x + 3 = 0

According to Vieta's theorem, the sum of the roots is equal to the negation of the coefficient of the second-to-last term divided by the coefficient of the leading term, and the product of the roots is equal to the constant term divided by the coefficient of the leading term.

In this case: - Coefficient of the second-to-last term: 5 - Coefficient of the leading term: 2 - Constant term: 3

Using the Vieta's theorem: - Sum of roots = -5/2 - Product of roots = 3/2

Therefore, the sum of the roots is -5/2 and the product of the roots is 3/2.

Conclusion:

The Vieta's theorem provides a useful tool for finding the sum and product of the roots of a polynomial equation without explicitly solving for the roots. It is a fundamental result in algebra and is applicable to polynomial equations of any degree.