Mathematics 2004 JAMB Past Questions - Question 11: Find the values of x where the curve Y = x³ + 2x² - 5x -6 crosses the x-axis

Correct Answer

C

Explanation

To find the values of x where the curve Y = x³ + 2x² - 5x - 6 crosses the x-axis, we need to find the values of x when Y is equal to zero.Setting Y = 0, we have the equation:0 = x³ + 2x² - 5x - 6To solve this equation, we can use various methods such as factoring, synthetic division, or numerical methods. In this case, let's use factoring.By trying different values of x, we find that x = -2 is a root of the equation. Therefore, (x + 2) is a factor of the equation.Using polynomial long division or synthetic division, we can divide the equation by (x + 2) to find the remaining quadratic equation:(x³ + 2x² - 5x - 6) ÷ (x + 2) = x² - x - 3Now, we can solve the quadratic equation x² - x - 3 = 0 by factoring or using the quadratic formula.Factoring the quadratic equation, we have:(x - 3)(x + 1) = 0Setting each factor equal to zero, we find two additional roots:x - 3 = 0 --> x = 3x + 1 = 0 --> x = -1Therefore, the curve Y = x³ + 2x² - 5x - 6 crosses the x-axis at x = -2, x = 3, and x = -1.