1. **Problem:** Find the distinct roots of the quadratic equation $x^2 - 5x + 6 = 0$. 2. **Formula:** For a quadratic equation $ax^2 + bx + c = 0$, the roots are given by the quadratic formula: $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ 3. **Step:** Calculate the discriminant: $$\Delta = b^2 - 4ac = (-5)^2 - 4 \times 1 \times 6 = 25 - 24 = 1$$ 4. **Step:** Since $\Delta > 0$, the equation has two distinct real roots. 5. **Step:** Calculate the roots: $$x_1 = \frac{5 + \sqrt{1}}{2} = \frac{5 + 1}{2} = 3$$ $$x_2 = \frac{5 - \sqrt{1}}{2} = \frac{5 - 1}{2} = 2$$ 6. **Answer:** The distinct roots are $x = 3$ and $x = 2$. This problem demonstrates how to find distinct roots using the quadratic formula by evaluating the discriminant and solving for $x$.