Question

Решите по теореме Виета:

Answer 1

Ответ:

если +40, то через Виету не решается :(

Объяснение:

Answer 2

Для того, чтобы использовать теорему Виета, нужно убедиться, что уравнение вообще имеет корни. Найдём дискриминант квадратного трёхчлена:

D = 4 - 2*4*40 = - 316;

D < 0, значит, корней у данного уравнения нет.

Ответ: корней нет.

Answer 3

The Vieta's Theorem

Vieta's theorem is a fundamental result in algebra that establishes a relationship between the coefficients and roots of a polynomial equation. It states that for a polynomial equation of degree n with coefficients a_n, a_n-1, ..., a₁, a₀, the sum of the roots is equal to the negation of the coefficient of the (n-1)-th term, and the product of the roots is equal to the constant term divided by the coefficient of the leading term.

Mathematically, for a polynomial equation of the form:

a_nxⁿ + a_n-1x^n-1 + ... + a₁x + a₀ = 0

The Vieta's theorem can be stated as:

Sum of the roots: x₁ + x₂ + ... + x_n = -a_n-1/a_n

Product of the roots: x₁ * x₂ * ... * x_n = (-1)ⁿ * a₀/a_n

Now, let's solve an example using Vieta's theorem.

Example:

Let's solve the quadratic equation x² - 9x + 20 = 0 using Vieta's theorem.

According to Vieta's theorem, the sum of the roots is equal to the negation of the coefficient of the linear term, and the product of the roots is equal to the constant term divided by the coefficient of the quadratic term.

In this case, the coefficient of the linear term is -9 and the constant term is 20.

Sum of the roots: x₁ + x₂ = -(-9)/1 = 9

Product of the roots: x₁ * x₂ = 20/1 = 20

Therefore, the sum of the roots is 9 and the product of the roots is 20.

Please let me know if you need any further assistance!