Question

Solve the following equation by identifying all of its roots including any imaginary numbers and multiple roots.

(x2 - 1)(x2 + 2)(x + 3)(x - 4)(x + 1) = 0

Answer 1

Answer: x = {-1, 1, -i√2, i√2, -3, 4}

Explanation:

Answer 2

Answer: x = {-1, 1, -i√2, i√2, -3, 4}

Explanation:

(x² - 1)(x² + 2)(x + 3)(x - 4)(x+1)=0

Set each factor equal to zero and solve.

x² - 1 = 0 → x² = 1 → x = ±1

x² + 2 = 0 → x² = -2 → x = ± i√2

x + 3 = 0 → x = -3

x - 4 = 0 → x = 4

x + 1 = 0 → x = -1 (note that -1 is a duplicate - solved from the first factor)