Final answer:
The zero of the function f(x) = 4x² - 12x + 9 is x = 3/2.
Step-by-step explanation:
The zero of the function can be found by setting f(x) equal to zero and solving for x. In this case, the function is given by f(x) = 4x² - 12x +9.
To find the zero, we set f(x) = 0:
4x² - 12x +9 = 0
We can solve this equation by factoring or by using the quadratic formula. In this case, factoring is not possible, so we will use the quadratic formula:
x = (-b ± √(b²-4ac)) / (2a)
In the quadratic formula, a is the coefficient of x², b is the coefficient of x, and c is the constant term.
Using the values from our function, a = 4, b = -12, and c = 9, we can substitute into the quadratic formula:
x = (-(-12) ± √((-12)²-4(4)(9))) / (2(4))
Simplifying the expression inside the square root:
x = (12 ± √(144-144)) / 8
x = (12 ± 0) / 8
Since the square root simplifies to 0, we are left with:
x = 12/8
x = 3/2
Therefore, the zero of the function f(x) = 4x² - 12x + 9 is x = 3/2.
Learn more about Finding zeros of a quadratic function