This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
To solve the inequality x^2 - 3x - 4 < 0, we first find the roots of the corresponding quadratic equation. Step 1: Find the roots of the quadratic equation x^2 - 3x - 4 = 0. We can factor the quadratic expression: x^2 - 3x - 4 = 0 We look for two numbers that multiply to -4 and add to -3. These numbers are -4 and 1. (x - 4)(x + 1) = 0 Setting each factor to zero gives the roots: x - 4 = 0 x = 4 x + 1 = 0 x = -1 The roots are x = -1 and x = 4. Step 2: Determine the interval where the inequality x^2 - 3x - 4 < 0 is true. The quadratic expression x^2 - 3x - 4 represents a parabola that opens upwards because the coefficient of x^2 is positive (1 > 0). For a parabola opening upwards, the expression is negative (less than zero) between its roots. Therefore, the inequality x^2 - 3x - 4 < 0 is satisfied when x is between -1 and 4. The solution set is -1 < x < 4. Step 3: Match the solution with the given options. The solution set is \x -1 < x < 4\, which corresponds to option A. The final answer is A. \x -1 < x < 4\. That's 2 down. 3 left today — send the next one.