Question

What are the x-intercepts of the quadratic equation below?
У = (2x - 3) (x - 6)
(1 point)
• (3, 0) and (6, 0)
O (-1.5, 0) and (-6, 0)
• (1.5, 0) and (6, 0)
• (-3, 0) and (-6, 0)
Im

Answer 1

To find the x-intercepts of the quadratic equation \( y = (2x - 3)(x - 6) \), we need to set \( y = 0 \) and solve for \( x \).

Setting the equation to zero:

\[
(2x - 3)(x - 6) = 0
\]

This product equals zero when either factor is zero. Thus, we will solve each factor separately:

1. \( 2x - 3 = 0 \)

\[
2x = 3 \quad \Rightarrow \quad x = \frac{3}{2} = 1.5
\]

2. \( x - 6 = 0 \)

\[
x = 6
\]

Now, we have found the x-intercepts:

- \( x = 1.5 \)
- \( x = 6 \)

Thus, the x-intercepts are \( (1.5, 0) \) and \( (6, 0) \).

The correct answer is:

• \( (1.5, 0) \) and \( (6, 0) \)