1. **State the problem:** Determine if the quadratic equation $x^2 - 5x + 6 = 0$ has distinct real roots. 2. **Recall the formula:** For a quadratic equation $ax^2 + bx + c = 0$, the discriminant $\Delta$ is given by: $$\Delta = b^2 - 4ac$$ 3. **Important rule:** - If $\Delta > 0$, the equation has two distinct real roots. - If $\Delta = 0$, the equation has exactly one real root (a repeated root). - If $\Delta < 0$, the equation has no real roots (complex roots). 4. **Identify coefficients:** Here, $a = 1$, $b = -5$, and $c = 6$. 5. **Calculate the discriminant:** $$\Delta = (-5)^2 - 4 \times 1 \times 6 = 25 - 24 = 1$$ 6. **Interpret the result:** Since $\Delta = 1 > 0$, the quadratic equation has two distinct real roots. **Final answer:** The equation $x^2 - 5x + 6 = 0$ has distinct real roots.