Question

Where does f(x) = 3x2 – 11x – 4 intersect the x-axis?

Answer 1

x= -1/3 (negative x-intercept)
x=4 (positive x-intercept)

Answer 2

f(x) intersect the x-axis ate ( 4 , 0 ) and ( -1/3 , 0)

Explanation:

Given function,
`f(x)=3x^2-11x-4`

We need to find this function cuts x-axis at what point.

let,
`y=3x^2-11x-4`

We know that points on x-axis has y-coordinate equal to 0.

So, we put y = 0 to find value of x.

By putting y = 0, we get

`0=3x^2-11x-4`

`3x^2-11x-4=0`

solving by quadratic formula,

`x=(-b\pm√(b^2-4ac))/(2a)`

`x=(-(-11)\pm√((-11)^2-4*3*(-4)))/(2*3)`

`x=(11\pm√(121+48))/(6)`

`x=(11\pm√(169))/(6)`

`x=(11\pm13)/(6)`

`x=(11+13)/(6)\:\:and\:\:x=(11-13)/(6)`

`x=(24)/(6)\:\:and\:\:x=(-2)/(6)`

`x=4\:\:and\:\:x=(-1)/(3)`

Therefore, f(x) intersect the x-axis ate ( 4 , 0 ) and ( -1/3 , 0)