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JAMB Mathematics 1998 Question 13

Question 13

Inequalities

Find the range of values of m for which the roots of the equation 3x2 − 3mx + (m2 − m − 3) = 0 are real.

  1. A.−1 ≤ m ≤ 7
  2. B.−2 ≤ m ≤ 6
  3. C.−3 ≤ m ≤ 9
  4. D.−4 ≤ m ≤ 8
Show the answer and explanation

Answer: B (−2 ≤ m ≤ 6)

Explanation

Real roots need b² − 4ac ≥ 0: 9m² − 12(m² − m − 3) ≥ 0, i.e. m² − 4m − 12 ≤ 0, so (m − 6)(m + 2) ≤ 0 and −2 ≤ m ≤ 6.