Set 8: Quadratic Equations

Choice A is correct. Choice A is the correct answer. For a parabola opening upward ($a=1$) to be always positive, it must never touch the x-axis. This means no real roots. 1. Discriminant $\Delta < 0$. 2. $k^2 - 4(1)(9) < 0$. 3. $k^2 - 36 < 0$. 4. Roots are $\pm 6$. Test regions: Between -6 and 6 (e.g., $k=0$, $-36 < 0$, True). 5. Range: $-6 < k < 6$. Choice B is incorrect. Choice C is incorrect. Choice D is incorrect.