Solve the cubic equation using factoring and the quadratic formula.
-$$x ^ { 3 } + 64 = 0$$
A) $\{ - 4,2 \pm 2 \mathrm { i } \sqrt { 3 } \}$

B) $\{ - 4 , - 2 \pm 2 \mathrm { i } \sqrt { 6 } \}$

C) $\{ - 4,2 \pm 2 \mathrm { i } \sqrt { 5 } \}$

D) $\{ - 4 , - 2 \pm 2 i \}$

Question

Solve the cubic equation using factoring and the quadratic formula.
-$$x ^ { 3 } + 64 = 0$$
A) $\{ - 4,2 \pm 2 \mathrm { i } \sqrt { 3 } \}$

B) $\{ - 4 , - 2 \pm 2 \mathrm { i } \sqrt { 6 } \}$

C) $\{ - 4,2 \pm 2 \mathrm { i } \sqrt { 5 } \}$

D) $\{ - 4 , - 2 \pm 2 i \}$

Quizplus · Accepted Answer

First, rewrite the equation as $x^3 = -64$, then factor it as $(x + 4)(x^2 - 4x + 16) = 0$. The roots are $x = -4$ and using the quadratic formula on $x^2 - 4x + 16 = 0$ gives $x = 2 \pm 2i\sqrt{3}$.

Solve the Cubic Equation Using Factoring and the Quadratic Formula x3+64=0x ^ { 3 } + 64 = 0x3+64=0

Solve the Cubic Equation Using Factoring and the Quadratic Formula $x ^ { 3 } + 64 = 0$