Solution — 2018 Question 1 Quadratic Equations & Inequalities

For two distinct roots, the discriminant must be positive

$\begin{matrix} b^{2} - 4 a c & > 0 \\ {(k - 6)}^{2} - 4 (- 2) (3 k) & > 0 \\ k^{2} - 12 k + 36 + 24 k & > 0 \\ k^{2} + 12 k + 36 & > 0 \\ (k + 6) (k + 6) & > 0 \end{matrix}$

inequality graph

$k < - 6 ∎ or x > - 6 ∎$