Lemmara logoLemmaraWorked solution

4PM1/02R Jun 2019, Question 1: The Discriminant and Nature of Roots

Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 2R · Calculator · 7 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Cubic f(x) = (x − 3)[x² + (p − 2)x + q] with f(0) = −12; find q, then find the p values giving exactly one real root.

Summarised in our own words. Use the official paper for the exact wording and any diagrams.

Part (a) · 2 marks

Use f(0) = −12 to find the value of q.

  1. 1f(0) = (0 − 3)(0 + 0 + q) = −3q
  2. 2−3q = −12
  3. 3q = 4

Answerq = 4

Part (b) · 5 marks

Find the range of p for which f(x) = 0 has only one real root.

  1. 1x = 3 is one root, so x² + (p − 2)x + 4 = 0 must have no real roots
  2. 2b² − 4ac < 0: (p − 2)² − 4 × 1 × 4 < 0
  3. 3Critical values: p² − 4p − 12 = 0 ⇒ (p − 6)(p + 2) = 0 ⇒ p = 6, −2
  4. 4Choose the inside region: −2 < p < 6

Answer−2 < p < 6

Stuck on a step? Read the free lesson: The Discriminant and Nature of Roots

Practise more the discriminant and nature of roots questions

Real 4PM1 past-paper questions, marked on your working like the exam, with a worked solution for every part.

Practise free on Lemmara

More past-paper questions on the discriminant and nature of roots

Also searched as: 4PM1 2R June 2019 · 4PM1/02R · 4pm1 jun19 2r · question 1.
Lemmara is an independent study tool, not affiliated with or endorsed by Pearson Edexcel. The worked solutions are Lemmara’s own.