Answer
x= $\frac{-2}{3}$
Work Step by Step
Another word for zeros is the x-intercept. An x-intercept is where the line crosses the x-axis. For this to happen, the y-value must be 0, so to find the zeros of the function, the equation must equal 0.
0 = $\sqrt {3x + 2}$
Overall, we want to separate the x from all other constants. The first step would be to get rid of the square root. We can do this by squaring both sides.
$0^{2}$ = $(\sqrt {3x + 2})^{2}$
This gets:
0 = 3x + 2
We then want to subtract 2 from both sides.
0 - 2 = 3x + 2 - 2
This gets:
-2 = 3x
We then want to divide both sides by 3 to get the x alone.
$\frac{-2}{3}$ = $\frac{3x}{3}$
This gets:
$\frac{-2}{3}$ = x
Since x = $\frac{-2}{3}$ when y = 0, x = $\frac{-2}{3}$ is a zero of the function.
