Question

What are all the real zeroes of y=(x−12)^3−7?

a. x = 12
b. x = 12 ± √7
c. x = 12 ± 7^(1/3)
d. None of these

Answer 1

The real zero of the function y = (x-12)^3 - 7 is found by setting y to zero and solving for x, which results in the answer x = 12 + 7^(1/3).

Step-by-step explanation:

The given function is y = (x-12)^3 - 7. To find the real zeroes of the function, we need to set y equal to zero. So, the equation becomes 0 = (x-12)^3 - 7. Solving for x, we add 7 to both sides, obtaining (x-12)^3 = 7. Taking the cube root of both sides gives us x-12 = 7^(1/3). Adding 12 to both sides, we find that the only real zero of the function is x = 12 + 7^(1/3).

Therefore, the answer is c. x = 12 + 7^(1/3), which is the real zero of the function.