Final answer:
The zeros of the function y = 6x²-x-2 are x = 1/2 and x = -2/3.
Step-by-step explanation:
The zeros of a function can be found by setting the function equal to zero and solving for x. In this case, we have the equation 6x²-x-2=0. To solve this quadratic equation, we can factor it or use the quadratic formula. Let's use the quadratic formula:
x = (-b ± √(b²-4ac)) / (2a)
For the equation 6x²-x-2=0, a = 6, b = -1, and c = -2. Plugging these values into the quadratic formula, we get:
x = (-(-1) ± √((-1)²-4(6)(-2))) / (2(6))
This simplifies to:
x = (1 ± √(1+48)) / 12
Which further simplifies to:
x = (1 ± √49) / 12
So the two zeros of the function are:
x = (1 + √49) / 12 = 1/2
x = (1 - √49) / 12 = -2/3
Learn more about Finding zeros of a quadratic function