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

Question

Quizplus · Accepted Answer

The equation $x^n - 1 = 0$ can be rewritten as $x^n = 1$. For any odd $n$, there is exactly one real solution to this equation, which is $x = 1$, because raising 1 to any power results in 1. Other roots of the equation, if $n > 1$, will be complex and occur in conjugate pairs, but there is always exactly one real root, making option C correct.

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