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WMA11/01 Jun 2019, Question 5: Solving Cubic Equations

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

The question, in short

Solve a cubic equation algebraically, then use that result to solve a related equation in y involving powers of y − 5.

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

Part (a) · 3 marks

Solve the cubic 2x³ + 3x² − 35x = 0 for all real x using algebra.

  1. 1x(2x² + 3x − 35) = 0
  2. 2x(2x − 7)(x + 5) = 0
  3. 3x = 0, x = 7/2, x = −5

Answerx = −5, 0, 7/2

Part (b) · 4 marks

Using part a, find every real y satisfying 2(y − 5)⁶ + 3(y − 5)⁴ − 35(y − 5)² = 0.

  1. 1Let x = (y − 5)², so the equation is 2x³ + 3x² − 35x = 0
  2. 2x = 0 gives (y − 5)² = 0, so y = 5
  3. 3x = −5 is impossible since (y − 5)² ≥ 0
  4. 4x = 7/2 gives (y − 5)² = 7/2, so y = 5 ± √(7/2)

Answery = 5, y = 5 + √(7/2), y = 5 − √(7/2)

Stuck on a step? Read the free lesson: Solving Cubic Equations

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