Question

Решить через теорему Виета 3х^2+5х-1=0

Answer 1

Может быть так:
3x^2 + 5x - 1 = 9x + 5x - 1 = 14x - 1 = 0
14x = 1

Answer 2

Solving the Quadratic Equation using Vieta's Theorem

To solve the quadratic equation 3x^2 + 5x - 1 = 0 using Vieta's theorem, we can use the following approach:

1. Identify the coefficients of the quadratic equation: - The coefficient of x^2 is 3. - The coefficient of x is 5. - The constant term is -1.

2. Apply Vieta's theorem: - Vieta's theorem states that for a quadratic equation ax^2 + bx + c = 0, the sum of the roots is equal to -b/a and the product of the roots is equal to c/a.

3. Find the sum of the roots: - In this case, the sum of the roots is equal to -b/a. - Plugging in the values from the equation, we have -5/3.

4. Find the product of the roots: - In this case, the product of the roots is equal to c/a. - Plugging in the values from the equation, we have -1/3.

5. Solve for the roots: - Let's assume the roots of the equation are r1 and r2. - We know that r1 + r2 = -5/3 and r1 * r2 = -1/3. - Using these equations, we can solve for the roots.

Let's calculate the roots using Vieta's theorem:

Sum of the roots (r1 + r2) = -5/3. Product of the roots (r1 * r2) = -1/3.

Using these equations, we can solve for the roots.