4PM1/01 Jun 2021, Question 1: The Discriminant and Nature of Roots
Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 1 · Calculator · 6 marks
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The question, in short
Determine all values of k for which the given quadratic in x, with coefficients involving k, has real roots.
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Solution · 6 marks
- 1Real roots: b² − 4ac ≥ 0
- 2(k + 5)² − 4 × 3(k + 2) × k ≥ 0
- 3k² + 10k + 25 − 12k² − 24k ≥ 0
- 411k² + 14k − 25 ≤ 0
- 5(11k + 25)(k − 1) ≤ 0, critical values −25/11 and 1
- 6−25/11 ≤ k ≤ 1
Answer−25/11 ≤ k ≤ 1
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