Determine the solution for x²-3x-28≥0

Answer:(- ∞, - 4 ] ∪ [7, + ∞ )Step-by-step explanation:Determine the zeros by equating to zero, that isx² - 3x - 28 = 0 ← in standard form(x - 7)(x + 4) = 0 ← in factored formEquate each factor to zero and solve for xx - 7 = 0 ⇒ x = 7x + 4 = 0 ⇒ x = - 4The zeros divide the domain into 3 intervals(- ∞ , - 4 ], [ - 4, 7 ], [ 7, + ∞)Choose a test point in each interval and compare value with required solutionx = - 5 : (- 5)² - 3(- 5) - 28 = 25 + 15 - 28 = 12 > 0x = 0 : 0 - 0 - 28 = - 28 < 0x = 10 : 10² - 3(10) - 28 = 100 - 30 - 28 = 42 > 0Solutions are the first and third interval, that isx ∈ (- ∞, - 4 ] ∪ [ - 7, + ∞)