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Further Mathematics Paper 2, Nov/Dec. 2009  
Questions: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Main
General Comments
Weakness/Remedies
Strength
Question 3

The roots of the equation 3x2 + 4x – 5  =  0  are a and b.  Find the equation whose roots are () and ().

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Observation

This question was reportedly attempted by majority of the candidates and they performed well in it.  They were able to show that if a and b are the roots, a + b = - and ab = - .  An equation whose new roots are (() can be formed by finding the sum ( + ) and products ()().  These were respectively    -  and  . 
Therefore the new equation =  +  +  = 0  º 15x2 + 34x + 18 = 0.

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