1. **Problem Statement:** Find the roots of the quadratic equation $$x^2 - 5x + 6 = 0$$. 2. **Formula Used:** The roots of a quadratic equation $$ax^2 + bx + c = 0$$ are given by the quadratic formula: $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ 3. **Identify coefficients:** Here, $$a = 1$$, $$b = -5$$, and $$c = 6$$. 4. **Calculate the discriminant:** $$\Delta = b^2 - 4ac = (-5)^2 - 4 \times 1 \times 6 = 25 - 24 = 1$$ 5. **Find the roots:** $$x = \frac{-(-5) \pm \sqrt{1}}{2 \times 1} = \frac{5 \pm 1}{2}$$ 6. **Evaluate each root:** - $$x_1 = \frac{5 + 1}{2} = \frac{6}{2} = 3$$ - $$x_2 = \frac{5 - 1}{2} = \frac{4}{2} = 2$$ 7. **Conclusion:** The roots of the quadratic equation are $$x = 3$$ and $$x = 2$$. These roots mean the parabola crosses the x-axis at these points.