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 $x ^ { n } - 1 = 0$ has exactly one real root.
C) The equation $\mathrm { x } ^ { \mathrm { n } } - 1 = 0$ has an odd number of nonreal roots.
D) The equation $x ^ { n } - 1 = 0$ has an even number of real roots.

Question

Quizplus · Accepted Answer

For any odd $n$, the equation $x^n - 1 = 0$ can be rewritten as $x^n = 1$. This equation always has exactly one real root, $x = 1$, because any odd power of a real number (other than zero) is positive if the base is positive and negative if the base is negative. Thus, the only real number $x$ that satisfies $x^n = 1$ for odd $n$ is $x = 1$.

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