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

Question

Quizplus · Accepted Answer

When $n$ is an odd number, the equation $x^n + 1 = 0$ can be rewritten as $x^n = -1$. This equation always has exactly one real root because raising any real number to an odd power can result in negative numbers, ensuring a real solution exists. The other roots, if $n > 1$, will be complex, but there is always at least one real root.

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

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