The problem asks us to find the x-intercepts of the quadratic function $h(x) = 3x^2 - 7x + 2$. We need to choose two correct x-intercepts from the list of options.

1. Problem Description

The problem asks us to find the x-intercepts of the quadratic function $h(x) = 3x^2 - 7x + 2$. We need to choose two correct x-intercepts from the list of options.

2. Solution Steps

First, we need to factor the quadratic expression $3x^2 - 7x + 2$. We are looking for two numbers that multiply to $(3)(2) = 6$ and add up to $-7$. These numbers are $-6$ and $-1$.

We can rewrite the middle term as $-7x = -6x - x$, so we have:

$3x^2 - 7x + 2 = 3x^2 - 6x - x + 2$

Now we factor by grouping:

$3x^2 - 6x - x + 2 = 3x(x - 2) - 1(x - 2) = (3x - 1)(x - 2)$

Thus, $h(x) = (3x - 1)(x - 2)$.

To find the x-intercepts, we set $h(x) = 0$ and solve for $x$:

$(3x - 1)(x - 2) = 0$

This gives us two solutions:

$3x - 1 = 0 \Rightarrow 3x = 1 \Rightarrow x = \frac{1}{3}$

$x - 2 = 0 \Rightarrow x = 2$

The x-intercepts are the points where the graph crosses the x-axis, i.e. when $y = h(x) = 0$. The x-intercepts are $(\frac{1}{3}, 0)$ and $(2, 0)$.

3. Final Answer

The x-intercepts are $(\frac{1}{3}, 0)$ and $(2, 0)$.