Question

Решить неравенство: 4х^2+16х≥0 , прошу вас помогите

Answer 1

4x² + 16x ≥0
4x(x + 4) ≥ 0
x (x + 4) ≥ 0
      +               -                 +
________________________
            - 4                 0
x ∈ ( - ∞ ; - 4]∪[0 ; + ∞)

Answer 2

Solving the Inequality 4x^2 + 16x ≥ 0

To solve the inequality 4x^2 + 16x ≥ 0, we can factor out the common term 4x, which gives us:

4x(x + 4) ≥ 0

Now, we can find the critical points by setting each factor equal to zero and solving for x:

1. 4x ≥ 0 => x ≥ 0 2. x + 4 ≥ 0 => x ≥ -4

So, the critical points are x = 0 and x = -4.

Next, we can use these critical points to test the intervals between them and determine the solution to the inequality.

- For x < -4: - If x < -4, both 4x and (x + 4) are negative, so their product is positive. Therefore, this interval satisfies the inequality.

- For -4 < x < 0: - If -4 < x < 0, 4x is negative and (x + 4) is positive, so their product is negative. Therefore, this interval does not satisfy the inequality.

- For x > 0: - If x > 0, both 4x and (x + 4) are positive, so their product is positive. Therefore, this interval satisfies the inequality.

Conclusion

The solution to the inequality 4x^2 + 16x ≥ 0 is x ≤ -4 or x ≥ 0.