By first expressing $3x-{{x}^{2}}-4$ in completed square form, show that $3x-{{x}^{2}}-4$ is always

Question

By first expressing $3x-{{x}^{2}}-4$ in completed square form, show that $3x-{{x}^{2}}-4$ is always negative for all real values of $x$. [2] Hence, or otherwise, without the use of a calculator, solve the inequality $\frac{\left( 3x-{{x}^{2}}-4 \right){{\left( x-1 \right)}^{2}}}{{{x}^{2}}-2x-5}\le 0$, leaving your answer in exact form. [4]

Accepted Answer

(i) Always negative (shown) (ii) $x 1 + \sqrt{6}$ \text{ or } $x = 1$

2017 HCI P1 Q3

2017 HCI P1 Q3

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