1. **State the problem:** Determine the nature of the roots of the quadratic equation $x^2 + x - 1 = 0$. 2. **Recall the formula:** The discriminant $\Delta$ of a quadratic equation $ax^2 + bx + c = 0$ is given by: $$\Delta = b^2 - 4ac$$ 3. **Important rule:** - If $\Delta > 0$, roots are real and distinct. - If $\Delta = 0$, roots are real and equal. - If $\Delta < 0$, roots are complex (not real). 4. **Calculate the discriminant:** For $x^2 + x - 1 = 0$, $a=1$, $b=1$, $c=-1$. $$\Delta = 1^2 - 4 \times 1 \times (-1) = 1 + 4 = 5$$ 5. **Interpret the result:** Since $\Delta = 5 > 0$, the roots are real and distinct. 6. **Check if roots are rational or irrational:** Since $\Delta = 5$ is not a perfect square, roots are irrational. **Final answer:** The roots of the quadratic equation $x^2 + x - 1 = 0$ are irrational and distinct.