what is the greatest zero of the function y=x^2-25+66
To find the greatest zero of the function y = x^2 - 25x + 66, we need to determine the values of x that make y equal to zero.
Step 1: Set the function equal to zero:
x^2 - 25x + 66 = 0
Step 2: Solve the quadratic equation. There are a few methods to solve quadratic equations, such as factoring, completing the square, or using the quadratic formula. In this case, let's use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
For our equation, a = 1, b = -25, and c = 66. Substituting these values into the formula:
x = (25 ± √((-25)^2 - 4(1)(66))) / (2(1))
Simplifying further:
x = (25 ± √(625 - 264)) / 2
x = (25 ± √(361)) / 2
x = (25 ± 19) / 2
This gives us two potential solutions:
x1 = (25 + 19) / 2 = 22
x2 = (25 - 19) / 2 = 3
Since we are looking for the greatest zero, the answer is x = 22.