Question

-x²-2x+3≤0 подалста помогите

Answer 1

Ответ:...

Объяснение:...

Answer 2

Solving the Inequality -x² - 2x + 3 ≤ 0

To solve the inequality -x² - 2x + 3 ≤ 0, we can use the quadratic formula to find the roots of the quadratic equation -x² - 2x + 3 = 0. The roots will help us identify the intervals where the inequality is satisfied.

The quadratic formula states that for a quadratic equation of the form ax² + bx + c = 0, the solutions for x are given by:

x = (-b ± √(b² - 4ac)) / (2a)

In this case, for the equation -x² - 2x + 3 = 0, the coefficients are: - a = -1 - b = -2 - c = 3

Using the quadratic formula, we can find the roots of the equation and then determine the intervals where the inequality is satisfied.

Finding the Roots of the Quadratic Equation

Applying the quadratic formula, the roots of the equation -x² - 2x + 3 = 0 are:

x = (-(-2) ± √((-2)² - 4*(-1)*3)) / (2*(-1))

x = (2 ± √(4 + 12)) / (-2)

x = (2 ± √16) / (-2)

x = (2 ± 4) / (-2)

So, the roots are: - x₁ = (2 + 4) / (-2) = 6 / (-2) = -3 - x₂ = (2 - 4) / (-2) = -2 / (-2) = 1

Analyzing the Inequality

Now that we have the roots of the equation, we can analyze the inequality -x² - 2x + 3 ≤ 0 in relation to these roots.

The inequality -x² - 2x + 3 ≤ 0 is satisfied when the quadratic expression is less than or equal to zero. This occurs in the intervals between and including the roots.

So, the solution to the inequality is: -3 ≤ x ≤ 1

Therefore, the inequality -x² - 2x + 3 ≤ 0 is satisfied when -3 ≤ x ≤ 1.

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