Solve the cubic equation using factoring and the quadratic formula.
-$$x ^ { 3 } + 1 = 0$$
A) $\{ - 1 , \pm i \}$

B) $\{ - 1 , - 1 \pm \mathrm { i } \sqrt { 3 } \}$

C) $\left\{ - 1 , \frac { 1 } { 2 } \pm \frac { \sqrt { 3 } } { 2 } \mathrm { i } \right\}$

D) $\{ - 1,1 \pm \mathrm { i } \sqrt { 3 } \}$

Question

Solve the cubic equation using factoring and the quadratic formula.
-$$x ^ { 3 } + 1 = 0$$
A) $\{ - 1 , \pm i \}$

B) $\{ - 1 , - 1 \pm \mathrm { i } \sqrt { 3 } \}$

C) $\left\{ - 1 , \frac { 1 } { 2 } \pm \frac { \sqrt { 3 } } { 2 } \mathrm { i } \right\}$

D) $\{ - 1,1 \pm \mathrm { i } \sqrt { 3 } \}$

Quizplus · Accepted Answer

First, rewrite the equation as $x^3 = -1$, which can also be expressed as $x^3 + 1 = 0$. This can be factored into $(x + 1)(x^2 - x + 1) = 0$. Solving $x + 1 = 0$ gives $x = -1$. For $x^2 - x + 1 = 0$, use the quadratic formula: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$, with $a = 1$, $b = -1$, and $c = 1$, yielding $x = \frac{1}{2} \pm \frac{\sqrt{3}}{2}i$.

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 $x ^ { 3 } + 1 = 0$