Final answer:
To find the zeros of the function g(x) = x²-11x+18, the quadratic equation x²-11x+18 = 0 needs to be solved. Using the quadratic formula, the solutions are x = 9 and x = 2.
Step-by-step explanation:
To find the zeros of the function g(x) = x²-11x+18, we need to solve the quadratic equation x²-11x+18 = 0. We can do this by factoring or by using the quadratic formula. Let's use the latter method:
The quadratic formula states that for an equation of the form ax²+bx+c = 0, the solutions are given by:
x = (-b ± √(b²-4ac))/(2a)
In our equation, a = 1, b = -11, and c = 18. Plugging in these values into the formula, we get:
x = (-(-11) ± √((-11)²-4(1)(18)))/(2(1))
Simplifying further, we have:
x = (11 ± √(121-72))/(2)
x = (11 ± √49)/(2)
x = (11 ± 7)/(2)
So the zeros of the function are x = 9 and x = 2.