Decide whether the statement is true or false. If it is false, tell why. -If k is a negative integer, then x² = k will have two irrational solutions. A) True B) False; the equation will have no real number solutions. C) False; the equation will have two rational solutions.

Question

Quizplus · Accepted Answer

The given equation is $x^{12} = k$, where $k$ is a negative integer. Since an even power of any real number (positive, negative, or zero) results in a positive number or zero, there are no real numbers $x$ that satisfy $x^{12} = k$ when $k$ is negative. Therefore, the equation will have no real number solutions.

Decide Whether the Statement Is True or False