Question

4x^2+11x-3<0 Плизззщщщщщщзззззз

Answer 1

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Answer 2

To solve the inequality 4x^2 + 11x - 3 < 0, we can follow these steps:

Step 1: Find the critical points. To find the critical points, we set the quadratic expression equal to zero and solve for x:

4x^2 + 11x - 3 = 0

Using factoring, quadratic formula, or completing the square, we can find the solutions to be:

x = (-11 ± √(11^2 - 4 * 4 * -3)) / (2 * 4) x = (-11 ± √(121 + 48)) / 8 x = (-11 ± √169) / 8 x = (-11 ± 13) / 8

Therefore, the critical points are x = -3/2 and x = 1/2.

Step 2: Create a number line. We'll draw a number line and mark the critical points on it:

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   -3/2        1/2
    |-----------|-----------|

Step 3: Test intervals. Choose a value from each interval and substitute it into the inequality to determine whether it is true or false.

For the interval to the left of -3/2 (e.g., x = -2), we have: 4(-2)^2 + 11(-2) - 3 = 4(4) - 22 - 3 = 16 - 22 - 3 = -9 Since -9 is less than 0, this interval satisfies the inequality.

For the interval between -3/2 and 1/2 (e.g., x = 0), we have: 4(0)^2 + 11(0) - 3 = -3 Since -3 is less than 0, this interval satisfies the inequality.

For the interval to the right of 1/2 (e.g., x = 2), we have: 4(2)^2 + 11(2) - 3 = 4(4) + 22 - 3 = 16 + 22 - 3 = 35 Since 35 is greater than 0, this interval does not satisfy the inequality.

Step 4: Determine the solution. Based on the results from Step 3, the solution to the inequality 4x^2 + 11x - 3 < 0 is:

-3/2 < x < 1/2

This means that x is any value between -3/2 and 1/2, excluding the endpoints.

I hope this helps! Let me know if you have any further questions.