Question

9x^3 - 18x^2 + 10x = 0

factor completely, and solve for each polynomial
[include all roots, real and complex numbers]

Answer 1

• {0, 1 + i/3, 1 - i/3}

Explanation:

• 9x³ - 18x² + 10x = 0
• x(9x² - 18x + 10) = 0
• x[9x² - 18x + 9 + 1) = 0
• x[(3x - 3)² + 1] = 0
• 1. x = 0,
• 2. (3x - 3)² = - 1 ⇒ 3x - 3 = ± i ⇒ 3x = 3 ± i ⇒ x = 1 ± i/3