Question

X^2+8x<0 Помогите пожалуйста

Answer 1

Ответ:

-x(x+8)=0

x1=0

x+8=0

x2=-8

Answer 2

Solving the Inequality X^2 + 8x < 0

To solve the inequality X^2 + 8x < 0, we can use the method of factoring and sign analysis.

Factoring the Quadratic Expression

First, let's factor the quadratic expression X^2 + 8x.

The factored form of the quadratic expression is x(x + 8).

Finding the Critical Points

To find the critical points, we set each factor equal to zero and solve for x:

1. Setting x = 0 gives us one critical point. 2. Setting x + 8 = 0 gives us the second critical point.

Solving x + 8 = 0 gives us x = -8.

So, the critical points are x = 0 and x = -8.

Sign Analysis

Now, we can perform a sign analysis to determine the intervals where the inequality is satisfied.

- For x < -8, both x and (x + 8) are negative, so the product x(x + 8) is positive. - For -8 < x < 0, x is negative and (x + 8) is positive, so the product x(x + 8) is negative. - For x > 0, both x and (x + 8) are positive, so the product x(x + 8) is positive.

Conclusion

Therefore, the solution to the inequality X^2 + 8x < 0 is -8 < x < 0.

This means that the inequality is satisfied when -8 < x < 0.