4PM1/01 Nov 2021, Question 2: The Discriminant and Nature of Roots
Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 1 · Calculator · 5 marks
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The question, in short
Given f(x) = 2x² + (p − 1)x − 2p with constant p, find the set of p values making f(x) = 0 have two distinct real roots.
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Solution · 5 marks
- 1b² − 4ac > 0: (p − 1)² − 4(2)(−2p) > 0
- 2p² + 14p + 1 > 0
- 3Critical values p = (−14 ± √(196 − 4))/2 = −7 ± 4√3
- 4Outside the roots: p < −7 − 4√3 or p > −7 + 4√3
Answerp < −7 − 4√3 or p > −7 + 4√3
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