Question

What are the x intercepts of the function below?
G (x) = (4x . - 1)(x+2)

Answer 1

To find the x-intercepts of the function \( G(x) = (4x - 1)(x + 2) \), we need to set the function equal to zero and solve for \( x \):

\[
G(x) = 0
\]

This gives us the equation:

\[
(4x - 1)(x + 2) = 0
\]

We can solve this by setting each factor equal to zero:

1. \( 4x - 1 = 0 \)
2. \( x + 2 = 0 \)

**Solving the first equation**:

\[
4x - 1 = 0
\]

Add 1 to both sides:

\[
4x = 1
\]

Now, divide by 4:

\[
x = \frac{1}{4}
\]

**Solving the second equation**:

\[
x + 2 = 0
\]

Subtract 2 from both sides:

\[
x = -2
\]

Thus, the x-intercepts of the function \( G(x) \) are:

\[
x = \frac{1}{4} \quad \text{and} \quad x = -2
\]

In summary, the x-intercepts are:

\[
\left( \frac{1}{4}, 0 \right) \quad \text{and} \quad (-2, 0)
\]