The value of `p` and `q` for which`p ,q` are the roots of the equation `x^2+p x+q=0` are

Explanation

To find the values of \( p \) and \( q \) for which \( p \) and \( q \) are the roots of the quadratic equation \( x^2 + px + q = 0 \), we can use Vieta's formulas. According to Vieta's formulas, for a quadratic equation of the form \( ax^2 + bx + c = 0 \), the sum and product of the roots can be expressed as follows:

1. The sum of the roots \( r_1 + r_2 = -\frac{b}{a} \)
2. The product of the roots \( r_1 \cdot r_2 = \frac{c}{a} \)

In our case, the equation is \( x^2 + px + q = 0 \), where \( a = 1 \), \( b = p \), and \( c = q \).

### Step 1: Write down the equations based on Vieta's formulas
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