Two equations 1 and 2 are given in each question. On the basis of these equations you have to decide the relation between p and q and give answer.
`p=(-10)^2`
`q^2+q-9900=0`

Options

A. If no relation can be decided between p and q
B. If `p gt q`
C. If `s gt p`
D. If p=q

Answer

To solve the given problem, we need to evaluate the two equations provided and determine the relationship between \( p \) and \( q \).

### Step 1: Calculate \( p \)

Given:
\[ p = (-10)^2 \]

Calculating \( p \):
\[ p = 100 \]

### Step 2: Solve for \( q \) using the quadratic equation

The second equation is:
\[ q^2 + q - 9900 = 0 \]

To solve for \( q \), we can use the quadratic formula:
\[ q = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
where \( a = 1 \), \( b = 1 \), and \( c = -9900 \).

### Step 3: Calculate the discriminant

First, we calculate the discriminant \( D \):
\[ D = b^2 - 4ac = 1^2 - 4 \cdot 1 \cdot (-9900) \]
\[ D = 1 + 39600 = 39601 \]

### Step 4: Calculate \( q \)

Now substituting back into the quadratic formula:
\[ q = \frac{-1 \pm \sqrt{39601}}{2 \cdot 1} \]

Calculating \( \sqrt{39601} \):
\[ \sqrt{39601} = 199 \]

Thus, we have:
\[ q = \frac{-1 \pm 199}{2} \]

Calculating the two possible values for \( q \):
1. \( q_1 = \frac{-1 + 199}{2} = \frac{198}{2} = 99 \)
2. \( q_2 = \frac{-1 - 199}{2} = \frac{-200}{2} = -100 \)

### Step 5: Compare \( p \) and \( q \)

Now we have two possible values for \( q \):
- \( q_1 = 99 \)
- \( q_2 = -100 \)

Since \( p = 100 \):
- For \( q_1 = 99 \): \( p > q_1 \)
- For \( q_2 = -100 \): \( p > q_2 \)

### Conclusion

In both cases, \( p \) is greater than both possible values of \( q \). Therefore, we can conclude:
\[ p > q \]