Question

The maximum number of real roots of the equation $x^{2n}-1=0$ is

• A. $2$
• B. $3$
• C. $n$
• D. $2n$

Answer 1

The correct option is A $2$

Let $f\left(x\right)=x^{2n}-1$
$f(-x)=x^{2n}-1$, obviously there is only one variation of sign each in $f\left(x\right)$ and $f(-x)$.
Therefore, the equation has at most two real roots one positive and one negative.