1. **State the problem:** Find the zeros of the function $f(x) = 2x^2 - 10.2x + 5.8$. Zeros are values of $x$ where $f(x) = 0$. 2. **Formula used:** To find zeros of a quadratic $ax^2 + bx + c = 0$, use the quadratic formula: $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ Important: The discriminant $\Delta = b^2 - 4ac$ determines the nature of roots. 3. **Identify coefficients:** Here, $a=2$, $b=-10.2$, $c=5.8$. 4. **Calculate discriminant:** $$\Delta = (-10.2)^2 - 4 \times 2 \times 5.8 = 104.04 - 46.4 = 57.64$$ 5. **Calculate roots:** $$x = \frac{-(-10.2) \pm \sqrt{57.64}}{2 \times 2} = \frac{10.2 \pm 7.59}{4}$$ 6. **Find each zero:** $$x_1 = \frac{10.2 + 7.59}{4} = \frac{17.79}{4} = 4.4475$$ $$x_2 = \frac{10.2 - 7.59}{4} = \frac{2.61}{4} = 0.6525$$ 7. **Round to nearest thousandth:** $$x_1 \approx 4.448$$ $$x_2 \approx 0.653$$ **Final answer:** The zeros of $f(x)$ are approximately $x = 4.448$ and $x = 0.653$.