Question

X²+2x-8=0 теорема виета сделайте прошу с решением

Answer 1

$\displaystyle\bf\\x^{2} +2x-8=0\\\\Teorema \ Vieta:\\\\x_{1} +x_{2} =-2\\\\x_{1} \cdot x_{2} =-8\\\\x_{1} =-4 \ \ ; \ \ x_{2} =2\\\\Otvet: \ -4 \ ; \ 2$

Answer 2

Ответ:

4;-2

Объяснение:

x²+2x-8=0

x1+x2=b

x1*x2=c

-2+4=2

4*(-2)= -8

X1= -2

x2=4

Answer 3

Equation and Vieta's Theorem

The given equation is x² + 2x - 8 = 0. To solve this equation, we can use Vieta's theorem, which relates the coefficients of a polynomial equation to its roots.

According to Vieta's theorem, for a quadratic equation ax² + bx + c = 0 with roots x₁ and x₂, the following relationships hold:

1. The sum of the roots is equal to the negation of the coefficient of the linear term divided by the coefficient of the quadratic term: x₁ + x₂ = -b/a. 2. The product of the roots is equal to the constant term divided by the coefficient of the quadratic term: x₁ * x₂ = c/a.

In our equation, the coefficient of the quadratic term is 1, the coefficient of the linear term is 2, and the constant term is -8. Applying Vieta's theorem, we can find the sum and product of the roots.

Solution

1. Sum of the roots: - The sum of the roots is equal to the negation of the coefficient of the linear term divided by the coefficient of the quadratic term. - In our equation, a = 1 and b = 2. - Therefore, the sum of the roots is x₁ + x₂ = -2/1 = -2.

2. Product of the roots: - The product of the roots is equal to the constant term divided by the coefficient of the quadratic term. - In our equation, a = 1 and c = -8. - Therefore, the product of the roots is x₁ * x₂ = -8/1 = -8.

Now, let's solve the equation using the quadratic formula to find the exact values of the roots.

Quadratic Formula

The quadratic formula is given by:

x = (-b ± √(b² - 4ac)) / (2a)

For our equation x² + 2x - 8 = 0, the coefficients are a = 1, b = 2, and c = -8.

Substituting these values into the quadratic formula, we get:

x = (-2 ± √(2² - 4 * 1 * -8)) / (2 * 1)

Simplifying further:

x = (-2 ± √(4 + 32)) / 2

x = (-2 ± √36) / 2

x = (-2 ± 6) / 2

This gives us two possible solutions:

1. x₁ = (-2 + 6) / 2 = 4 / 2 = 2 2. x₂ = (-2 - 6) / 2 = -8 / 2 = -4

Therefore, the solutions to the equation x² + 2x - 8 = 0 are x₁ = 2 and x₂ = -4.

Verification

To verify the solutions, we can substitute them back into the original equation and check if they satisfy it.

For x = 2: 2² + 2 * 2 - 8 = 4 + 4 - 8 = 0

For x = -4: (-4)² + 2 * (-4) - 8 = 16 - 8 - 8 = 0

Both solutions satisfy the equation, confirming that x₁ = 2 and x₂ = -4 are indeed the solutions.

Therefore, the solutions to the equation x² + 2x - 8 = 0 are x₁ = 2 and x₂ = -4.