WMA11/01 Jan 2023, Question 4: The Discriminant and Nature of Roots
Pearson Edexcel International AS Level Mathematics · Pure Mathematics 1 (WMA11) · Calculator · 4 marks
The question, in short
For kx² + 6kx + 5 = 0 with k nonzero and no real roots, find the range of values of k.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Solution · 4 marks
- 1No real roots: b² − 4ac < 0
- 2(6k)² − 4 × k × 5 < 0, so 36k² − 20k < 0
- 34k(9k − 5) < 0, critical values k = 0 and k = 5/9
- 4k ≠ 0, so 0 < k < 5/9
Answer0 < k < 5/9
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