What are the x intercepts of the function below?

Question

G (x) = (4x . - 1)(x+2)
A. (1,0) and (2,0)
B. (0,25, 0) and (-2,0)
C. (-0,25, 0) and (2,0)
D. (-1,0) and (2,0)

Answer 1

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

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

This equation will be true when either factor is zero:

1. Set \( 4x - 1 = 0 \): \[ 4x = 1 \implies x = \frac{1}{4} \]

2. Set \( x + 2 = 0 \): \[ x = -2 \]

Thus, the x-intercepts are \( \left(\frac{1}{4}, 0\right) \) and \( (-2, 0) \).

Now, examining the answer choices:

A. \( (1,0) \) and \( (2,0) \) - Incorrect B. \( (0,25, 0) \) and \( (-2,0) \) - Incorrect C. \( (-0,25, 0) \) and \( (2,0) \) - Incorrect D. \( (-1,0) \) and \( (2,0) \) - Incorrect

None of the options provided are correct. The correct x-intercepts are \( \left(\frac{1}{4}, 0\right) \) and \( (-2, 0) \).