Question

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

Answer 1

Answer:

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

Step-by-step 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,

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

$x=\frac{-(-11)\pm\sqrt{(-11)^2-4\times3\times(-4)}}{2\times3}$

$x=\frac{11\pm\sqrt{121+48}}{6}$

$x=\frac{11\pm\sqrt{169}}{6}$

$x=\frac{11\pm13}{6}$

$x=\frac{11+13}{6}\:\:and\:\:x=\frac{11-13}{6}$

$x=\frac{24}{6}\:\:and\:\:x=\frac{-2}{6}$

$x=4\:\:and\:\:x=\frac{-1}{3}$

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

Answer 2

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