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WMA11/01 Jan 2020, Question 5: Cubic Equations and Curve Meetings

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 1 (WMA11) · Calculator · 7 marks

The question, in short

Solve a cubic equation in x by algebraic methods, then use that result to solve a related equation in y involving powers of (y + 3).

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

Part (a) · 3 marks

Determine every value of x satisfying 20x³ − 50x² − 30x = 0, showing algebraic working.

  1. 1Factor out 10x: 10x(2x² − 5x − 3) = 0
  2. 2Factorise: 10x(2x + 1)(x − 3) = 0
  3. 3x = 0, x = −½, x = 3

Answerx = 0, x = −1/2, x = 3

Part (b) · 4 marks

Using the earlier result, determine all real y satisfying 20(y + 3)^(3/2) − 50(y + 3) − 30(y + 3)^(1/2) = 0.

  1. 1The equation is part (a) with x = (y + 3)^(1/2)
  2. 2So (y + 3)^(1/2) = 0, −½ or 3
  3. 3(y + 3)^(1/2) cannot be negative, so reject −½
  4. 4(y + 3)^(1/2) = 0 gives y = −3; (y + 3)^(1/2) = 3 gives y + 3 = 9, so y = 6

Answery = −3, y = 6

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