Question

Решить уравнение 2х^2 - х + 5 =0 Вещественных корней нет, а как найти комплексные корни ? Помогите пожалуйста )))

Answer 1

D = -39.
x1 = (1+√-39)/4 = (1+i√39)/4.= 0.25+√39/4 *i
x2 = (1-i√39)/4= 0.25-√39/4 *i.

Answer 2

Solving the Quadratic Equation for Complex Roots

To solve the quadratic equation 2x^2 - x + 5 = 0 for complex roots, we can use the quadratic formula. The quadratic formula states that for an equation in the form ax^2 + bx + c = 0, the solutions for x are given by:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, for the equation 2x^2 - x + 5 = 0, the coefficients are: - a = 2 - b = -1 - c = 5

Using the quadratic formula, we can find the complex roots of the equation.

Applying the Quadratic Formula

The solutions for x are given by: x = (-(-1) ± √((-1)^2 - 4*2*5)) / (2*2)

Solving this equation will give us the complex roots of the original quadratic equation.

Calculating the Complex Roots

Let's calculate the discriminant first: D = b^2 - 4ac D = (-1)^2 - 4*2*5 D = 1 - 40 D = -39

Now, we can use the quadratic formula to find the complex roots: x = (-(-1) ± √(-39)) / (2*2) x = (1 ± √(-39)) / 4

The square root of a negative number results in a complex number. Therefore, the complex roots of the given quadratic equation are: x = (1 + √(-39)) / 4 and x = (1 - √(-39)) / 4

These are the complex roots of the given quadratic equation.

I hope this helps! If you have any further questions or need additional assistance, feel free to ask.