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