Multiple choice

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

  1. $2$
  2. $3$
  3. $n$
  4. $2n$
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A Correct answer
Explanation

x^(2n) = 1. The real roots are x = 1 and x = -1. There are exactly 2 real roots regardless of the value of n (assuming n >= 1).

AI explanation

Rewriting the equation gives x^(2n) = 1. For any real number x, raising it to an even power 2n always results in a non-negative value. The only real numbers that satisfy x^(2n) = 1 are x = 1 and x = -1. Therefore, the maximum number of real roots is 2.

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