Final answer:
To find the zeros of the given quadratic function, we use the quadratic formula. The zeros of the function F(x) = -5x^2 + 10x + 8 are (-10 + 2√65)/(-10) and (-10 - 2√65)/(-10).
Step-by-step explanation:
To find the zeros of a quadratic function, we need to solve the equation F(x) = -5x^2 + 10x + 8 = 0. We can do this by factoring, completing the square, or using the quadratic formula. In this case, the equation does not easily factor, so we can use the quadratic formula. The quadratic formula is given by x = (-b ± √(b^2 - 4ac))/(2a), where the quadratic function is in the form ax^2 + bx + c = 0.
For the given function F(x) = -5x^2 + 10x + 8, the coefficients are a = -5, b = 10, and c = 8. Substituting these values into the quadratic formula, we have:
x = (-10 ± √(10^2 - 4(-5)(8)))/(2(-5))
Simplifying further:
x = (-10 ± √(100 + 160))/( -10)
x = (-10 ± √(260))/( -10)
x = (-10 ± √260)/ (-10)
x = (-10 ± 2√65)/ (-10)
Therefore, the zeros of the function F(x) = -5x^2 + 10x + 8 are x = (-10 + 2√65)/(-10) and x = (-10 - 2√65)/(-10).
Learn more about Finding zeros of a quadratic function