Moderate -0.3 This is a straightforward application of the discriminant condition b²-4ac < 0 for no real roots, requiring students to solve a simple quadratic inequality. While it involves a parameter k, the method is standard and commonly practiced, making it slightly easier than average.
Correct discriminant of given quadratic equation (may be implied). Not given if just seen in quadratic formula.
\(9 - 4k^2 < 0\) leading to two critical values of \(k\)
M1
Finds two critical values of \(k\) from their discriminant. Or for one correct inequality (may come from only one c.v.)
\(k > \frac{3}{2}\) [or] \(k < -\frac{3}{2}\)
A1
oe e.g. set notation \(\{k: k < -\frac{3}{2}\} \cup \{k: k > \frac{3}{2}\}\)
## Question 1:
| Answer | Mark | Guidance |
|--------|------|----------|
| $\Delta = 3^2 - 4(k)(k)$ | B1 | Correct discriminant of given quadratic equation (may be implied). Not given if **just** seen in quadratic formula. |
| $9 - 4k^2 < 0$ leading to two critical values of $k$ | M1 | Finds two critical values of $k$ from **their** discriminant. **Or** for one correct inequality (may come from only one c.v.) |
| $k > \frac{3}{2}$ [or] $k < -\frac{3}{2}$ | A1 | oe e.g. set notation $\{k: k < -\frac{3}{2}\} \cup \{k: k > \frac{3}{2}\}$ |
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1 The quadratic equation $k x ^ { 2 } + 3 x + k = 0$ has no real roots.
Determine the set of possible values of $k$.
\hfill \mbox{\textit{OCR PURE Q1 [3]}}