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2024 DHS Promo Q5

2024 DHS Promo Q5

8 marks
Promo
  1. Find, using an algebraic method, the exact roots of the equation \({\left| 3x^2 + 5x - 8 \right| = 4 - x}\).[4]
  2. On the same axes, sketch the curves with equations \({y = \left| 3x^2 + 5x - 8 \right|}\) and \({y = 4 - x}\).
    Hence solve exactly the inequality \({\left| 3x^2 + 5x - 8 \right| < 4 - x}\).[4]

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Answer:(a) \(x=-1-\sqrt5\), \(-2\), \(\dfrac23\), or \(-1+\sqrt5\) (b) \(-1-\sqrt5<x<-2\) or \(\dfrac23<x<-1+\sqrt5\)

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