4PM1/02 Jun 2022, Question 1: The Discriminant and Nature of Roots
Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 2 · Calculator · 4 marks
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The question, in short
Find the values of k, k ≠ 0, for which 2kx² + 5kx + 5k − 3 = 0 has real roots.
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Solution · 4 marks
- 1Real roots: b² − 4ac ≥ 0
- 2(5k)² − 4(2k)(5k − 3) ≥ 0
- 3−15k² + 24k ≥ 0 ⇒ 3k(8 − 5k) ≥ 0
- 4Critical values 0 and 8/5; k ≠ 0, so 0 < k ≤ 8/5
Answer0 < k ≤ 8/5
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