2025 RVHS Promo Q5
2025 RVHS Promo Q5
Junior College 1
8 marks
Do not use a calculator in answering this question.
- Show that \(x^2-x+3\) is always positive for all real values of \(x\).[1]
Solve the inequality,
\(\frac{x\left(x^2-x+3\right)}{10-x-3x^2}\leq 0.\)
[4]Hence solve the inequality,
\(\frac{|x|\left(x^2-|x|+3\right)}{10-|x|-3x^2}\leq 0.\)
[3]
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Answer:(b) \(-2<x \leq 0\) or \(x>\frac{5}{3} \)(c) \(x=0\) or \(x<-\dfrac53\) or \(x>\dfrac53\)
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