Solve.
-$x ^ { 3 } + 11 x + x ^ { 2 } + 11 = 0$
A) $\{ - 1 , - i \sqrt { 11 } , i \sqrt { 11 } \}$
B) $\{ 1 , - \sqrt { 11 } , \sqrt { 11 } \}$
C) $\{ - 1 , - \sqrt { 11 } , \sqrt { 11 } \}$
D) $\{ 1 , - i \sqrt { 11 } , i \sqrt { 11 } \}$

Question

Quizplus · Accepted Answer

First, rearrange the equation in descending order of powers: $x^3 + x^2 + 11x + 11 = 0$. Factoring by grouping, we get $x^2(x + 1) + 11(x + 1) = 0$, which simplifies to $(x^2 + 11)(x + 1) = 0$. Solving for $x$, we find the roots to be $x = -1$, $x = -i\sqrt{11}$, and $x = i\sqrt{11}$.

Solve - x3+11x+x2+11=0x ^ { 3 } + 11 x + x ^ { 2 } + 11 = 0x3+11x+x2+11=0

Solve
- $x ^ { 3 } + 11 x + x ^ { 2 } + 11 = 0$