Question

Use the x-intercept method to find all real solutions of the equation. x³8x² + 9x + 18-0 ▸ a. x = -1, 3, or 6 b. x= 1, 3, or 6 x = 1, -3, or 6 d. x = -1, 3, or - 6 Please select the best answer from the choices provided ΟΑ​

Answer 1

To use the x-intercept method to find the solutions of the equation x³ + 8x² + 9x + 18 = 0, we need to factor the equation, set each factor to zero, and solve for x. One possible way to do this is:

x³ + 8x² + 9x + 18 = 0

(x + 2)(x² + 6x + 9) = 0 (by factoring out a common factor of (x + 2))

(x + 2)(x + 3)(x + 3) = 0 (by factoring the quadratic trinomial x² + 6x + 9)

Therefore, the solutions of the equation are x = -2 (with multiplicity 1) and x = -3 (with multiplicity 2). Thus, the correct answer is d. x = -1, 3, or -6.