L6FM Homework 2 Due Mon 19.9.16

Total: 20 marks. Show all working out. Those not showing mathematical rigour will be penalised.

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1. Write in the from $a(x+b)^2 + c$
   i.e. complete the square: \[3x^2-7x-20\]

   [3 marks]

2. Simplify \[ \frac{3}{x^2-5x +4} - \frac{5}{x^2-16} \]

   [4 marks]

3. Simplify as far as possible: \[ \frac{15}{\sqrt {5}} - \frac{46}{2\sqrt{7} - \sqrt{5}} \]

   [4 marks]

4. Solve $6x^2+x-12>0$

   [3 marks]

5. Solve $5+x+x^2>0$

   [3 marks]

6. Solve \[ x^2 = 4+5xy \\ x=5y +1 \]

   [3 marks]