The quadratic equation corresponding to the roots 2 + sqrt(5) and 2 - sqrt(5) is ________.

Step 1 (Find the Sum of Roots): Let the roots be $\alpha =2+\sqrt{5}$ and $\beta =2-\sqrt{5}$. The sum of the roots is:

Step 2 (Find the Product of Roots): Using the difference of squares identity $(A+B)(A-B)=A^2-B^2$:

Step 3 (Formulate the Quadratic Equation): Any quadratic equation with sum of roots $S$ and product of roots $P$ is given by:

Substituting the values:

Step 4 (Conclusion): The corresponding quadratic equation is exactly x^2 - 4x - 1 = 0.