Solve. Express any nonreal complex numbers with i notation.
-$$x ^ { 4 } - 6 x ^ { 2 } - 27 = 0$$
A) $x = \pm 3 , \pm i \sqrt { 3 }$
B) $x = 3 , i \sqrt { 3 }$
C) $x = - 9,3$
D) $x = \pm \sqrt { 3 } , \pm 3 \mathrm { i }$

Question

Quizplus · Accepted Answer

This equation can be solved by substituting $y = x^2$, turning it into a quadratic equation $y^2 - 6y - 27 = 0$. Solving this quadratic equation gives $y = 9$ and $y = -3$. Substituting back $x^2 = y$, we get $x^2 = 9$ which gives $x = \pm 3$, and $x^2 = -3$ which gives $x = \pm i\sqrt{3}$. Therefore, the solutions are $x = \pm 3, \pm i\sqrt{3}$.

Solve Express Any Nonreal Complex Numbers with I Notation x4−6x2−27=0x ^ { 4 } - 6 x ^ { 2 } - 27 = 0x4−6x2−27=0

Solve Express Any Nonreal Complex Numbers with I Notation $x ^ { 4 } - 6 x ^ { 2 } - 27 = 0$