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4MA1/1HR Jan 2022, Question 19: The Quadratic Formula and Completing the Square

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1HR (Higher) · Calculator · 3 marks

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The question, in short

Use the equation with a cube root and fourth power to find m, then rewrite 3x² + 12x + 19 in completed-square form with integers a, b, c.

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

Part (a) · 1 mark

Find the value of m from the given equation involving a cube root of 1/x raised to the fourth power.

  1. 11 ÷ ∛(x⁴) = x^m
  2. 2∛(x⁴) = x^(4/3)
  3. 3So 1 ÷ x^(4/3) = x^(−4/3)
  4. 4x^(−4/3) = x^m
  5. 5m = −4/3

Answer−4/3

Part (b) · 2 marks

Express 3x² + 12x + 19 as a(x + b)² + c where a, b and c are integers.

  1. 1Take 3 out of the x terms: 3(x² + 4x) + 19
  2. 2Complete the square: x² + 4x = (x + 2)² − 4
  3. 33((x + 2)² − 4) + 19 = 3(x + 2)² − 12 + 19
  4. 4= 3(x + 2)² + 7

Answer3(x + 2)² + 7

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