1. **State the problem:** We need to find the nature of the roots of the quadratic equation $x^2 + 5x - 6 = 0$ using the discriminant. 2. **Recall the quadratic equation and discriminant formula:** A quadratic equation is of the form $ax^2 + bx + c = 0$. The discriminant $\Delta$ is given by: $$\Delta = b^2 - 4ac$$ 3. **Identify coefficients:** Here, $a = 1$, $b = 5$, and $c = -6$. 4. **Calculate the discriminant:** $$\Delta = 5^2 - 4 \times 1 \times (-6) = 25 + 24 = 49$$ 5. **Interpret the discriminant:** - If $\Delta > 0$, roots are real and distinct. - If $\Delta = 0$, roots are real and equal. - If $\Delta < 0$, roots are complex conjugates. Since $\Delta = 49 > 0$, the roots of the equation are real and distinct. **Final answer:** The quadratic equation $x^2 + 5x - 6 = 0$ has two real and distinct roots.