Question

Cоставьте квадратное уравнение по его корням х1=-2, х2= С помощью теоремы Виета

Answer 1

$x^2+px+q=0\\\\ \left \{ {{x_1\cdot x_2=q} \atop {x_1+x_2=-p}} \right. \\\\x_1\cdot x_2=-2\cdot \sqrt5\\\\x_1+x_2=-2+\sqrt5\\\\x^2+(2-\sqrt5)x-2\sqrt5=0$

Answer 2

Forming a Quadratic Equation Using Vieta's Theorem

To form a quadratic equation using Vieta's theorem, we can use the following approach:

Given the roots of the quadratic equation as x1 = -2 and x2 = -8, we can use Vieta's theorem to form the quadratic equation.

Vieta's theorem states that for a quadratic equation of the form ax^2 + bx + c = 0 with roots x1 and x2, the sum of the roots is equal to -b/a and the product of the roots is equal to c/a.

Using Vieta's theorem, we can derive the quadratic equation as follows:

1. Sum of the roots: - The sum of the roots x1 and x2 is equal to -b/a. - In this case, x1 + x2 = -2 + (-8) = -10. - This gives us the equation: x1 + x2 = -b/a = -10.

2. Product of the roots: - The product of the roots x1 and x2 is equal to c/a. - In this case, x1 * x2 = (-2) * (-8) = 16. - This gives us the equation: x1 * x2 = c/a = 16.

Using the above information, we can form the quadratic equation as follows:

- The sum of the roots equation: x1 + x2 = -10 - The product of the roots equation: x1 * x2 = 16

By substituting the values of x1 + x2 and x1 * x2 into the equations, we can form the quadratic equation.

Quadratic Equation: - The quadratic equation formed using Vieta's theorem with roots x1 = -2 and x2 = -8 is: - x^2 - (-10)x + 16 = 0 - Simplifying, we get: x^2 + 10x + 16 = 0

Therefore, the quadratic equation is x^2 + 10x + 16 = 0, based on the roots x1 = -2 and x2 = -8.