Final answer:
To find the zeros of the quadratic function g(x) = 4x^2 - x + 5, you need to solve the equation 4x^2 - x + 5 = 0. However, this quadratic equation has no real solutions, so the function does not have any zeros.
Step-by-step explanation:
To find the zeros of the quadratic function g(x) = 4x^2 - x + 5, we need to solve the equation 4x^2 - x + 5 = 0. This equation can be solved using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a). In this case, a = 4, b = -1, and c = 5. Plugging the values into the formula, we have:
- x = (-(-1) ± √((-1)^2 - 4(4)(5))) / (2(4))
- x = (1 ± √(1 - 80)) / 8
- x = (1 ± √(-79)) / 8
Since there is a negative value under the square root, there are no real solutions to this quadratic equation. Therefore, the function g(x) = 4x^2 - x + 5 has no zeros.