Question

What are the ,begin emphasis,two,end emphasis, zeros of the quadratic function defined by the expression 9 x squared minus 4?

Answer options with 7 options
A.
x equals negative 3

B.
x equals negative 2-thirds

C.
x equals negative 2-ninths

D.
x equals 0

E.
x equals 2-ninths

F.
x equals 2-thirds

G.
x equals 3

Answer 1

To find the zeros of the quadratic function defined by the expression \( 9x^2 - 4 \), we need to set the function equal to zero and solve for \( x \):

\[
9x^2 - 4 = 0
\]

We can rearrange this equation:

\[
9x^2 = 4
\]

Then, divide both sides by 9:

\[
x^2 = \frac{4}{9}
\]

Next, we take the square root of both sides:

\[
x = \pm \sqrt{\frac{4}{9}} = \pm \frac{2}{3}
\]

Thus, the zeros of the function are:

\[
x = \frac{2}{3} \quad \text{and} \quad x = -\frac{2}{3}
\]

Now, let's match these values to the answer choices provided:

- The option corresponding to \( x = \frac{2}{3} \) is **F. x equals 2-thirds**
- The option corresponding to \( x = -\frac{2}{3} \) is **B. x equals negative 2-thirds**

Thus, the correct answers are:

**B** and **F**.