1. **Problem:** One root of the quadratic equation $x^2 - (k^2 - 4k + 4)x + 9 = 0$ is the additive inverse of the other. Find $k$. 2. **Formula and rules:** For a quadratic equation $ax^2 + bx + c = 0$ with roots $r_1$ and $r_2$, the sum of roots is $r_1 + r_2 = -\frac{b}{a}$ and the product is $r_1 r_2 = \frac{c}{a}$. 3. **Given condition:** One root is the additive inverse of the other, so if roots are $r$ and $-r$, then their sum is $r + (-r) = 0$. 4. **Apply sum of roots:** From the equation, sum of roots is $k^2 - 4k + 4$ (since $a=1$, $b=-(k^2 - 4k + 4)$, so sum is $-b = k^2 - 4k + 4$). 5. **Set sum to zero:** $$k^2 - 4k + 4 = 0$$ 6. **Solve quadratic:** $$k^2 - 4k + 4 = (k - 2)^2 = 0$$ 7. **Root:** $$k = 2$$ **Answer:** $k = 2$. --- **Final answer:** $k = 2$ (option b).