Quadratic Roots C9B7Cf

1. **State the problem:** We need to find the roots of the quadratic equation $$w^2 - 8w + 16 = 0$$. 2. **Recall the quadratic formula:** For an equation $$aw^2 + bw + c = 0$$, the roots are given by $$w = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$. 3. **Identify coefficients:** Here, $$a = 1$$, $$b = -8$$, and $$c = 16$$. 4. **Calculate the discriminant:** $$\Delta = b^2 - 4ac = (-8)^2 - 4 \times 1 \times 16 = 64 - 64 = 0$$. 5. **Since $$\Delta = 0$$, there is exactly one real root (a repeated root).** 6. **Calculate the root:** $$w = \frac{-(-8) \pm \sqrt{0}}{2 \times 1} = \frac{8 \pm 0}{2} = \frac{8}{2} = 4$$. 7. **Final answer:** $$w = 4$$.