Moderate -0.3 This is a standard discriminant question requiring students to apply b²-4ac > 0 for two distinct real roots, then solve a quadratic inequality. It's slightly easier than average because it's a routine textbook exercise with clear steps (set up discriminant condition, expand, solve inequality, remember k≠0 for quadratic), though the inequality solving and consideration of k≠0 adds minor complexity beyond pure recall.
3 The equation \(k x ^ { 2 } + ( k - 6 ) x + 2 = 0\) has two distinct real roots. Find the set of possible values of the constant \(k\), giving your answer in set notation.
Attempt discriminant; Obtain correct 3 term expression; Find critical values for \(k\), eg by attempting to solve discriminant \(> 0\); Chooses 'outside region' of their inequality; A1 for stating \(k \neq 0\) OR A1 for \((-\infty, 2) \cup (18, \infty)\); Any correct set notation
| $b^2 - 4ac = (k-6)^2 - 8k$; $k^2 - 20k + 36$; $k = 2, k = 18$; $k < 2, k > 18$; $(-\infty, 0) \cup (0, 2) \cup (18, \infty)$ | M1, A1, M1, M1, A2 | Attempt discriminant; Obtain correct 3 term expression; Find critical values for $k$, eg by attempting to solve discriminant $> 0$; Chooses 'outside region' of their inequality; A1 for stating $k \neq 0$ OR A1 for $(-\infty, 2) \cup (18, \infty)$; Any correct set notation |
3 The equation $k x ^ { 2 } + ( k - 6 ) x + 2 = 0$ has two distinct real roots. Find the set of possible values of the constant $k$, giving your answer in set notation.
\hfill \mbox{\textit{OCR H240/01 2018 Q3 [6]}}