1. **State the problem:** Calculate the discriminant and determine the nature of the roots for the quadratic equation $$2x^2 + 3x + 1 = 0$$. 2. **Recall the formula for the discriminant:** For a quadratic equation $$ax^2 + bx + c = 0$$, the discriminant $$\Delta$$ is given by: $$\Delta = b^2 - 4ac$$ 3. **Identify coefficients:** Here, $$a = 2$$, $$b = 3$$, and $$c = 1$$. 4. **Calculate the discriminant:** $$\Delta = 3^2 - 4 \times 2 \times 1 = 9 - 8 = 1$$ 5. **Interpret the discriminant:** - If $$\Delta > 0$$, the quadratic has two distinct real roots. - If $$\Delta = 0$$, the quadratic has exactly one real root (a repeated root). - If $$\Delta < 0$$, the quadratic has two complex conjugate roots. Since $$\Delta = 1 > 0$$, the quadratic equation has two distinct real roots. **Final answer:** The discriminant is $$1$$, and the quadratic has two distinct real roots.