4024/12 May/Jun 2021, Question 21: The Quadratic Formula and Completing the Square
Cambridge O Level Mathematics 4024 · Paper 12 (Non-calculator) · Non-calculator · 3 marks
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The question, in short
Complete the square on x² + 10x + 6 and then use the completed-square form to solve the equation x² + 10x + 6 = 0, giving the answer as p ± √q.
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Part (a) · 2 marks
Rewrite x² + 10x + 6 as (x + a)² + b, stating the values of a and b.
- 1x² + 10x = (x + 5)² − 25
- 2x² + 10x + 6 = (x + 5)² − 25 + 6
- 3= (x + 5)² − 19
Answer(x + 5)² − 19
Part (b) · 1 mark
Using part (a), solve x² + 10x + 6 = 0 and express the solution in the form p ± √q.
- 1(x + 5)² − 19 = 0 → (x + 5)² = 19
- 2x + 5 = ±√19
- 3x = −5 ± √19
Answer−5 ± √19
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Also searched as: 4024/12/M/J/21 · 4024_s21_qp_12 · 4024 s21 12 · question 21.
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