Question

A graph of `f\left(x\right)=6x^{2}-11x+3` is shown on the grid.

What are the zeros of `f`?

answer choices:
3
11/12
1/3 and 3/2 
2 and 9

Answer 1

To find the zeros of a function, you need to set the function equal to zero and solve for x. In this case, the function is f(x) = 6x^2 - 11x + 3.

So, setting f(x) equal to zero:
6x^2 - 11x + 3 = 0

To find the zeros, we can either factor the quadratic equation or use the quadratic formula. Factoring may not be possible for all quadratic equations, so let's use the quadratic formula:

x = [-(-11) ± √((-11)^2 - 4(6)(3))] / 2(6)
x = [11 ± √(121 - 72)] / 12
x = [11 ± √49] / 12
x = [11 ± 7] / 12

Now, we have two possible solutions:
x1 = (11 + 7) / 12 = 18 / 12 = 3/2
x2 = (11 - 7) / 12 = 4 / 12 = 1/3

Therefore, the zeros of the function f(x) = 6x^2 - 11x + 3 are 3/2 and 1/3. The correct answer choice would be "1/3 and 3/2".