WMA11/01 Jan 2020, Question 8: When a Line Meets, Touches or Misses a Curve
Pearson Edexcel International AS Level Mathematics · Pure Mathematics 1 (WMA11) · Calculator · 6 marks
The question, in short
Line y = k(2x − 1) and curve y = x² + 2x + 11; find the range of k for which the line misses the curve entirely.
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Solution · 6 marks
- 1Equate: k(2x − 1) = x² + 2x + 11
- 2Rearrange: x² + (2 − 2k)x + 11 + k = 0
- 3No intersection: b² − 4ac < 0, so (2 − 2k)² − 4(11 + k) < 0
- 4Simplify: 4k² − 12k − 40 < 0, so k² − 3k − 10 < 0, (k − 5)(k + 2) < 0
- 5Critical values k = 5 and k = −2; inside region: −2 < k < 5
Answer−2 < k < 5
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