**Quadratic Equation with Roots 1/p and 1/q**

To find the quadratic equation with roots 1/p and 1/q, we can use the concept of Vieta's formulas. Vieta's formulas provide a relationship between the coefficients of a quadratic equation and its roots.

**Vieta's Formulas**
Vieta's formulas state that for a quadratic equation of the form ax^2 + bx + c = 0 with roots p and q, the following relationships hold:
- Sum of the roots: p + q = -b/a
- Product of the roots: pq = c/a

**Given Information**
We are given that the roots of the quadratic equation x^2 + 2x + 1 = 0 are p and q. From this information, we can determine the values of a, b, and c.

**Determining the values of a, b, and c**
Comparing the given equation x^2 + 2x + 1 = 0 with the standard quadratic equation ax^2 + bx + c = 0, we can equate the corresponding coefficients:

- Coefficient of x^2: 1 = a
- Coefficient of x: 2 = b
- Constant term: 1 = c

Therefore, the values of a, b, and c are 1, 2, and 1, respectively.

**Finding the Quadratic Equation with Roots 1/p and 1/q**
Using Vieta's formulas, we can establish the relationships between the coefficients and the roots:

- Sum of the roots: 1/p + 1/q = -b/a = -2/1 = -2
- Product of the roots: (1/p)(1/q) = c/a = 1/1 = 1

To create a quadratic equation with roots 1/p and 1/q, we can use the following steps:

1. Start with the equation (x - 1/p)(x - 1/q) = 0 since the roots are 1/p and 1/q.
2. Expand the equation:
x^2 - (1/p + 1/q)x + (1/p)(1/q) = 0
3. Simplify the equation using the values from Vieta's formulas:
x^2 - (-2)x + 1 = 0
4. Final quadratic equation:
x^2 + 2x + 1 = 0

Therefore, the quadratic equation with roots 1/p and 1/q is x^2 + 2x + 1 = 0.