Further Mathematics Paper 2, WASSCE (PC), 2017

Question 1

 

Find the range of values of m for which mx2 + 2mx – 3 = 0 has real roots.

Observation

 

  The Chief Examiner reported that this question was not popular with majority of the candidates. Most of them found it difficult to sole. They were solving for equal roots rather than real roots. For real roots 4m2 + 12m ≥ 0 and factorizing will yield m( m + 3) ≥ 0. If we investigate, the range of values of m for which the expression has equal roots are m > 0 and
m ≤ - 3.