Sure! Let's go step by step to **find the roots of a quadratic equation**. --- ### **Step 1: Write the Quadratic Equation** A quadratic equation is in the form: **ax² + bx + c = 0** Let's take a **third quadratic equation** (as you requested), so, for example: **3x² - 5x + 2 = 0** --- ### **Step 2: Use the Quadratic Formula** The roots of a quadratic equation can be found using the quadratic formula: **x = [-b ± √(b² - 4ac)] / (2a)** For our equation: - *a* = 3 - *b* = -5 - *c* = 2 Let's substitute these values in: - Calculate the discriminant: b² - 4ac = (-5)² - 4×3×2 = 25 - 24 = **1** - Plug into the formula: x = [5 ± √1] / 6 --- ### **Step 3: Solve for the Roots** Now, compute the two roots: - √1 = 1 So, x₁ = (5 + 1) / 6 = **6/6 = 1** x₂ = (5 - 1) / 6 = **4/6 = 2/3** --- ### **Final Summary** **To find the roots of a quadratic equation**, 1. **Write it in standard form (ax² + bx + c = 0).** 2. **Apply the quadratic formula and calculate the discriminant.** 3. **Solve for the two roots.** **For the equation 3x² - 5x + 2 = 0, the roots are x = 1 and x = 2/3.**