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2026 RI P1 Q6

2026 RI P1 Q6

Junior College 2
8 marks
  1. Show that \(2x^2-4x+3\) is always positive for all real values of \(x\).
    Without using a calculator, solve the inequality \(\frac{x^2-10x+3}{(2x+1)(x-3)}\geq x\).[6]
  2. Hence solve the inequality \(\frac{x^2-10|x|+3}{(2|x|+1)(|x|-3)}>|x|\).[2]

Solution:

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Answer:(a) \(x<-\frac12\) or \(1\leq x<3\) (b) \(-3<x<-1\) or \(1<x<3\)

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