Question

X^2+13x+40 меньше или равно 0 Помогите пожалуйста,с объяснением.

Answer 1

X^2+13x+40=0
Д=b^2-4ac
Д=169-160=9, 2 корня
х=-b+-√Д : 2a
х1= -13+3 :2= -5
х2= -13-3:2= -8

Answer 2

Solving the Quadratic Inequality X^2 + 13x + 40 ≤ 0

To solve the quadratic inequality X^2 + 13x + 40 ≤ 0, we can use the following steps:

1. Find the Roots of the Quadratic Equation: First, we find the roots of the related quadratic equation X^2 + 13x + 40 = 0. The roots can be found using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a), where a = 1, b = 13, and c = 40.

The roots of the equation are: - x = (-13 + √(13^2 - 4*1*40)) / (2*1) - x = (-13 - √(13^2 - 4*1*40)) / (2*1)

These roots will help us understand the behavior of the quadratic function.

2. Analyze the Inequality: After finding the roots, we can analyze the inequality X^2 + 13x + 40 ≤ 0 based on the roots of the related equation.

3. Solve the Inequality: Using the information from the roots, we can determine the solution to the inequality X^2 + 13x + 40 ≤ 0.

Let's proceed with these steps to solve the given quadratic inequality.

Finding the Roots of the Quadratic Equation

The roots of the quadratic equation X^2 + 13x + 40 = 0 are: - x = (-13 + √(13^2 - 4*1*40)) / (2*1)- x = (-13 - √(13^2 - 4*1*40)) / (2*1)

Analyzing the Inequality

The inequality X^2 + 13x + 40 ≤ 0 can be analyzed based on the roots of the related equation.

Solving the Inequality

Based on the roots of the related equation, we can determine the solution to the inequality X^2 + 13x + 40 ≤ 0.