0580/22 May/Jun 2023, Question 12: Substitution
Cambridge IGCSE Mathematics 0580 · Paper 22 (Extended) · Calculator · 3 marks
اقرأ هذا الحل مشروحاً بالعربي ←
The question, in short
A quadratic equation ax² + b = 181 has x = 8 as one root, with a and b positive integers above 1. Determine b, then state the second root.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Part (a) · 2 marks
Using the fact that x = 8 satisfies the equation, work out the integer value of b.
- 1a × 8² + b = 181, so 64a + b = 181
- 2a = 2 (a > 1 and 64a < 181): b = 181 − 128
- 3b = 53
Answer53
Part (b) · 1 mark
Give the remaining value of x that also satisfies the equation.
- 1(−8)² = 8², so x = −8 also works
- 2x = −8
Answer−8
Stuck on a step? Read the free lesson: Substitution
Practise more substitution questions
Real 0580 past-paper questions, marked on your working like the exam, with a worked solution for every part.
Practise free on LemmaraMore past-paper questions on substitution
Also searched as: 0580/22/M/J/23 · 0580_s23_qp_22 · 0580 s23 22 · question 12.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.