Here's the step-by-step solution:
1. A quadratic equation is represented in the form of ax^2 + bx + c = 0.
2. The sum of the roots of the quadratic equation can be represented as -b/a, and the product of the roots as c/a.
4. We are given that the sum of the roots is -3 and the product is 2.
5. For the sake of simplicity, we consider the value of 'a' to be 1 in this scenario.
6. We then use the formulas of sum and product of roots to determine the values of 'b' and 'c'.
7. The coefficient 'b' will equal -a times the sum of the roots, which yields -(-3) = 3.
8. The coefficient 'c' will equal 'a' times the product of the roots, which yields 1*2 = 2.
9. Substituting the values a=1, b=3, and c=2 into the quadratic equation we get the final equation as x^2 + 3x + 2 = 0.
This is how we can derive the quadratic equation from the given sum and the product of the roots.