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8 marksCubic Functions and Equations

CAPE Pure Mathematics Unit 1 · May/June 2016 · Paper 2 · Question 2(c)(ii)

The roots of the equation 2x³ – 5x² + 4x + 6 = 0 are α, β and γ.

Hence, or otherwise, determine an equation with integer coefficients which has roots 1/α², 1/β² and 1/γ². Note: (αβ)² + (αγ)² + (βγ)² = (αβ + αγ + βγ)² – 2αβγ (α + β + γ) and α² + β² + γ² = (α + β + γ)² – 2 (αβ + αγ + βγ).

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Other parts of this question

  1. 2(a)Solve the following equation for x: log₂(10 - x) + log₂x = 4.[6 marks]
  2. 2(b)Determine whether f is bijective, that is, both one-to-one and onto.[8 marks]
  3. 2(c)(i)State the values of α + β + γ, αβ + αγ + βγ and αβγ.[3 marks]

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