Show graphically the solution sets of the following inequalities:

(a) X square - 7 * h2 > 0
(b) 3X square - 5X - 2 > 0

To graphically represent the solution sets for the given inequalities, we need to plot the corresponding quadratic equations on a coordinate plane.

(a) x^2 - 7h^2 > 0:
To start, let's consider the graph of the equation x^2 - 7h^2 = 0, which is a parabola opened upwards.

Step 1: Plot the vertex of the parabola. The vertex is given by the equation x = -b/2a, where a and b are coefficients of x and x^2 in the quadratic equation. In this case, a = 1 and b = 0, so the vertex is (0, 0).

Step 2: Plot two other points symmetrically around the vertex. For simplicity, choose points to the left and right of the vertex. You can select any values of x and find corresponding values of h using the equation x^2 - 7h^2 = 0. For example, let's choose x = -1 and x = 1 as the points. Substituting these values, we get h = ±1/√7. So, the points are (-1, -1/√7) and (1, 1/√7).

Step 3: Draw a smooth curve passing through the points. Since the inequality x^2 - 7h^2 > 0 specifies that values of the equation are greater than zero, we need to shade the region above and below the parabola but excluding the parabola itself.

The graph of x^2 - 7h^2 > 0 would look like this:

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(b) 3x^2 - 5x - 2 > 0:
Similarly, let's graph the equation 3x^2 - 5x - 2 = 0.

Step 1: Calculate the vertex using x = -b/2a. Here, a = 3 and b = -5. Substituting these values gives x = 5/6.

Step 2: Find two other points symmetrically around the vertex. Choose x-values to the left and right of the vertex and calculate the corresponding h-values. For example, if we choose x = 0 and x = 2, substituting them into the equation gives h = -2/3 and h = 2/3, respectively. The points are (0, -2/3) and (2, 2/3).

Step 3: Draw a smooth curve through the points. Since the solution set is greater than zero, you need to shade the region above and below the parabola but exclude the parabola itself.

The graph of 3x^2 - 5x - 2 > 0 would look like this:

```
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```

These graphs give you a visual representation of the solution sets for the given inequalities.