Question

X²-3x+5=0 теорема виета сделайте с решением прошу

Answer 1

Ответ:

нет корней

Объяснение:

x²-3x+5=0

D=(-3)²-4.1.5=9-20=-11

Answer 2

Solving the Equation using Vieta's Theorem

To solve the equation x² - 3x + 5 = 0 using Vieta's theorem, we can consider the quadratic equation in the form ax² + bx + c = 0. Vieta's theorem states that for a quadratic equation with roots x₁ and x₂, the sum of the roots is equal to the negation of the coefficient of the linear term (b) divided by the coefficient of the quadratic term (a), and the product of the roots is equal to the constant term (c) divided by the coefficient of the quadratic term (a).

In this case, the coefficient of the quadratic term (a) is 1, the coefficient of the linear term (b) is -3, and the constant term (c) is 5. According to Vieta's theorem, the sum of the roots is equal to -b/a, and the product of the roots is equal to c/a.

Let's calculate the sum and product of the roots using Vieta's theorem:

Sum of the roots (x₁ + x₂) = -(-3)/1 = 3/1 = 3 Product of the roots (x₁ * x₂) = 5/1 = 5

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

Now, let's find the values of x₁ and x₂ using the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

For our equation, a = 1, b = -3, and c = 5. Substituting these values into the quadratic formula, we get:

x = (-(-3) ± √((-3)² - 4(1)(5))) / (2(1)) x = (3 ± √(9 - 20)) / 2 x = (3 ± √(-11)) / 2

Since the discriminant (√(b² - 4ac)) is negative, the equation has no real solutions. The roots are complex numbers.

Therefore, the equation x² - 3x + 5 = 0 has no real solutions.

I hope this helps! Let me know if you have any further questions.