Step 1: Identify the given roots. The roots are $r_1 = -3$ and $r_2 = 1$. Step 2: Calculate the sum of the roots. $$ \text{Sum of roots} = r_1 + r_2 = -3 + 1 = -2 $$ Step 3: Calculate the product of the roots. $$ \text{Product of roots} = r_1 \times r_2 = (-3) \times (1) = -3 $$ Step 4: Construct the quadratic equation using the formula $x^2 - (\text{sum of roots})x + (\text{product of roots}) = 0$. $$ x^2 - (-2)x + (-3) = 0 $$ Step 5: Simplify the equation. $$ x^2 + 2x - 3 = 0 $$ The constructed and simplified equation is $\boxed{x^2 + 2x - 3 = 0}$.