Moderate -0.5 This is a straightforward application of the discriminant condition b²-4ac < 0 for no real roots. It requires substituting values into a formula and solving a simple quadratic inequality, making it slightly easier than average but still requiring correct execution of a standard technique.
allow in quadratic formula or clearly looking for perfect square
\(k^2 - 4 \times 2 \times 18 < 0\) o.e.
M1
condone \(\leq\); or M1 for 12 identified as boundary
\(-12 < k < 12\)
A2
may be two separate inequalities; A1 for \(\leq\) used or for one 'end' correct; if two separate correct inequalities seen, isw for wrongly combining; condone \(b\) instead of \(k\); if no working, SC2 for \(k < 12\) and SC2 for \(k > -12\)
Total: 4 marks
# Question 8:
| Answer/Working | Mark | Guidance |
|---|---|---|
| $b^2 - 4ac$ soi | M1 | allow in quadratic formula or clearly looking for perfect square |
| $k^2 - 4 \times 2 \times 18 < 0$ o.e. | M1 | condone $\leq$; or M1 for 12 identified as boundary |
| $-12 < k < 12$ | A2 | may be two separate inequalities; A1 for $\leq$ used or for one 'end' correct; if two separate correct inequalities seen, isw for wrongly combining; condone $b$ instead of $k$; if no working, SC2 for $k < 12$ and SC2 for $k > -12$ |
| **Total: 4 marks** | | |
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8 Find the range of values of $k$ for which the equation $2 x ^ { 2 } + k x + 18 = 0$ does not have real roots.
\hfill \mbox{\textit{OCR MEI C1 2009 Q8 [4]}}