Solve the cubic equation using factoring and the quadratic formula.
-$$x ^ { 3 } - 1 = 0$$
A) $\{ 1 , \pm i \}$
B) $\{ 1 , - 1 \pm i \sqrt { 3 } \}$
C) $\left\{ 1 , - \frac { 1 } { 2 } \pm \frac { \sqrt { 3 } } { 2 } \mathrm { i } \right\}$
D) $\{ 1,1 \pm i \sqrt { 3 } \}$

Question

Quizplus · Accepted Answer

First, factor the equation as $x^3 - 1 = (x - 1)(x^2 + x + 1) = 0$. The root of $x - 1 = 0$ is $x = 1$. For $x^2 + x + 1 = 0$, use the quadratic formula to find the complex roots: $x = \frac{-1 \pm \sqrt{1^2 - 4(1)(1)}}{2(1)} = \frac{-1 \pm \sqrt{-3}}{2} = -\frac{1}{2} \pm \frac{\sqrt{3}}{2}i$.

Solve the Cubic Equation Using Factoring and the Quadratic Formula x3−1=0x ^ { 3 } - 1 = 0x3−1=0

Solve the Cubic Equation Using Factoring and the Quadratic Formula $x ^ { 3 } - 1 = 0$