For what values of k does the equation x² + kx + 9 = 0 have two distinct real solutions?

A quadratic has two distinct real solutions when its discriminant is positive. For $x^2 + kx + 9 = 0$, the discriminant is $k^2 - 4(1)(9) = k^2 - 36$. Requiring $k^2 - 36 > 0$ gives $k^2 > 36$, so $k > 6$ or $k < -6$, choice D. Choice A ($-6 < k < 6$) is the opposite case, where the discriminant is negative and there are no real solutions. Choice B gives a discriminant of exactly zero, which means a single repeated root, not two. Choice C ($k > 9$) uses the constant term instead of 6 and misses the negative values of $k$.