WMA11/01 Jan 2019, Question 9: Lines Meeting Curves: the Discriminant
Pearson Edexcel International AS Level Mathematics · Pure Mathematics 1 (WMA11) · Calculator · 7 marks
The question, in short
A constant c makes the equation 3/x + 5 = −2x + c have no real solutions; determine all c values for which this happens.
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Solution · 7 marks
- 1Multiply by x: 3 + 5x = −2x² + cx
- 2Rearrange: 2x² + (5 − c)x + 3 = 0
- 3No real roots: b² − 4ac < 0, so (5 − c)² − 24 < 0
- 4Critical values: 5 − c = ±√24, so c = 5 ± 2√6
- 5Take the inside region: 5 − 2√6 < c < 5 + 2√6
Answer5 − 2√6 < c < 5 + 2√6
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