Final answer:
To find the zeros of the function g(z) = 6z² - z - 1, you can use the quadratic formula. The zeros are z = 1/2 and z = -1/3.
Step-by-step explanation:
To find the zeros of the function g(z) = 6z² - z - 1, we need to solve the equation 6z² - z - 1 = 0.
We can solve this quadratic equation using factoring, completing the square, or the quadratic formula. In this case, let's use the quadratic formula.
The quadratic formula is given by: z = (-b ± √(b² - 4ac)) / (2a)
For our equation, a = 6, b = -1, and c = -1. Plugging these values into the quadratic formula gives us:
z = (-(-1) ± √((-1)² - 4(6)(-1))) / (2(6))
z = (1 ± √(1 + 24)) / 12
Simplifying further, we have:
z = (1 ± √25) / 12
z = (1 ± 5) / 12
So the two zeros of the function g(z) = 6z² - z - 1 are:
z = (1 + 5) / 12 = 6/12 = 1/2
z = (1 - 5) / 12 = -4/12 = -1/3