Further Mathematics Paper 2, Nov/Dec. 2010
 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 4

Find the equation whose roots are the squares of the roots of the equation
x2-mx+ n = O.

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Observation

The Chief Examiner reported that this question was well attempted by majority of candidates. However, one common error observed by the Chief Examiner was that some candidates did not equate their final result to zero.
Candidates were expected to show that if α² and β² are the roots of the equation X² - mx + n = 0, then α + β = m, αβ = n. If α² and β² are the roots of the new equation, then sum of roots is given by α² + β² = (α + β)² - 2 αβ = m² - 2n. Similarly, product of roots = α²β² = αβ² = n². Therefore the equation with roots α² and β² will be given in terms of m and n as X² - (m²-2n)x + n² = O. Some candidates wroteα + β = -m instead of m hence, they lost some marks.

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