Show that $4{{x}^{2}}-20x+35$ is always positive for all real values of $x$. [1] Hence, without usin

Question

Show that $4{{x}^{2}}-20x+35$ is always positive for all real values of $x$. [1] Hence, without using a calculator, solve the inequality $\frac{{{x}^{2}}-2x-3}{4{{x}^{3}}-20{{x}^{2}}+35x}>0$. [3] Use your answer to part (ii) to solve the inequality $\frac{{{x}^{2}}-2\left| x \right|-3}{4{{\left| x \right|}^{3}}-20{{x}^{2}}+35\left| x \right|}>0$. [2]

Accepted Answer

(i) Always positive (shown); (ii) -1 3; (iii) x > 3 or x < -3

2013 MJC P1 Q1

2013 MJC P1 Q1

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