Answer the question.
-If $\mathrm { n }$ is an even number, then which of the following statements is true?
A) The equation $\mathrm { x } ^ { \mathrm { n } } + 1 = 0$ has exactly one real root.
B) The equation $\mathrm { x } ^ { \mathrm { n } } + 1 = 0$ has $\mathrm { n } + 1$ roots.
C) The equation $\mathrm { x } ^ { \mathrm { n } } + 1 = 0$ has $\mathrm { n }$ nonreal roots.
D) The equation $x _ { n } + 1 = 0$ has at least one real root.

Question

Quizplus · Accepted Answer

For an even $n$, the equation $x^n + 1 = 0$ can be rewritten as $x^n = -1$. Since raising $x$ to an even power results in a non-negative number for any real $x$, the equation $x^n = -1$ cannot have real solutions. Therefore, all $n$ roots of the equation must be nonreal.

Answer the Question n\mathrm { n }n Is an Even Number, Then Which of the Following Statements

Answer the Question $\mathrm { n }$ Is an Even Number, Then Which of the Following Statements