Question

Which of the following equations has both −5 and 5 as possible values of z? Choose all answers that apply:

a. z²=36
b. z³=125
c. None of the above

Answer 1

The equation z²=36 has both -5 and 5 as possible values of z. None of the other equations have both -5 and 5 as possible values of z.

Step-by-step explanation:

The equation z²=36 has both -5 and 5 as possible values of z. This is because when we take the square root of 36, we get both 6 and -6, which are the positive and negative solutions for z. Therefore, answer choice a (z²=36) is correct.

On the other hand, the equation z³=125 does not have -5 as a possible value of z. When we take the cube root of 125, we only get the positive solution, which is 5. Therefore, answer choice b (z³=125) is incorrect.

So, the correct answer is a. z²=36 and none of the other equations have both -5 and 5 as possible values of z.