I. `p^(2)= 4`
II.` q^(2) + 4q =- 4`

Options

A. if p is greater than q.
B. if p is smaller than q.
C. if p is equal q.
D. if p is either equal to or greater than q.

Explanation

To solve the given equations and find the relationship between \( p \) and \( q \), we will follow these steps:

### Step 1: Solve for \( p \)
Given the equation:
\[ p^2 = 4 \]

To find \( p \), we take the square root of both sides:
\[ p = \pm \sqrt{4} \]
\[ p = \pm 2 \]

### Step 2: Solve for \( q \)
Now, we solve the equation:
\[ q^2 + 4q = -4 \]

First, we rearrange the equation to set it to zero:
\[ q^2 + 4q + 4 = 0 \]

Next, we can factor this quadratic equation:
\[ (q + 2)(q + 2) = 0 \]
or
\[ (q + 2)^2 = 0 \]

This gives us:
\[ q + 2 = 0 \]
Thus, solving for \( q \):
\[ q = -2 \]

### Step 3: Compare \( p \) and \( q \)
Now we have the values:
- \( p = 2 \) or \( p = -2 \)
- \( q = -2 \)

We can compare these values:
1. If \( p = 2 \), then \( p > q \) because \( 2 > -2 \).
2. If \( p = -2 \), then \( p = q \) because both are equal to -2.

Since \( p \) can take both values \( 2 \) and \( -2 \), we can conclude:
\[ p \geq q \]

### Final Answer
The relationship between \( p \) and \( q \) is:
\[ p \geq q \]