wikiHow Practice Problems and Answers to Solve a Cubic Equation 1. x^3 + 4x^2 - 7x + 2 = 0 2. x^3 - 6x^2 + 11x - 6 = 0 3. x^3 + x^2 - 6x + 6 = 0 4. x^3 - 5x^2 + 7x - 3 = 0 5. x^3 + 2x^2 + 3x + 2 = 0 6. x^3 - 4x^2 - 11x - 20 = 0 7. x^3 + x^2 + 7x + 7 = 0 8. x^3 - x^2 - 8x - 8 = 0 9. x^3 + 3x^2 + 8x + 24 = 0 10. x^3 - 2x^2 + 5x - 10 = 0 Answers: 1. x^3 + 4x^2 - 7x + 2 = 0 (x+2) (x^2 + 2x - 1) = 0 x = -2, x = (-1 + sqrt(3))/2, x = (-1 - sqrt(3))/2 2. x^3 - 6x^2 + 11x - 6 = 0 (x-6)(x^2 - x - 1) = 0 x = 6, x = (1 + sqrt(5))/2, x = (1 - sqrt(5))/2 3. x^3 + x^2 - 6x + 6 = 0 (x+3)(x^2 + 3x - 2) = 0 x = -3, x = (-2 + sqrt(2))/2, x = (-2 - sqrt(2))/2 4. x^3 - 5x^2 + 7x - 3 = 0 (x-1)(x^2 - 6x + 3) = 0 x = 1, x = (3 + sqrt(21))/2, x = (3 - sqrt(21))/2 5. x^3 + 2x^2 + 3x + 2 = 0 This equation has no real solutions. 6. x^3 - 4x^2 - 11x - 20 = 0 (x+4)(x^2 - 7x - 5) = 0 x = -4, x = (7 + sqrt(49 - 60))/2, x = (7 - sqrt(49 - 60))/2 7. x^3 + x^2 + 7x + 7 = 0 (x+7)(x^2 + x + 1) = 0 x = -7, x = (-1 + sqrt(-3))/2, x = (-1 - sqrt(-3))/2 Since sqrt(-3) is an imaginary number, there are no real solutions to this equation. 8. x^3 - x^2 - 8x - 8 = 0 (x-4)(x^2 + 4x + 2) = 0 x = 4, x = (-2 + sqrt(2))/2, x = (-2 - sqrt(2))/2 9. x^3 + 3x^2 + 8x + 24 = 0 (x+4)(x^2 + 4x + 6) = 0 x = -4, x = (-2 + sqrt(2))/2, x = (-2 - sqrt(2))/2 10. x^3 - 2x^2 + 5x - 10 = 0 (x-2)(x^2 - 3x + 5) = 0 x = 2, x = (3 + sqrt(5))/2, x = (3 - sqrt(5))/2 Page