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JAMB Mathematics 2000 Question 12

Question 12

Binary Operations

A binary operation * is defined by a*b = ab. If a*2 = 2 − a, find the possible value of a.

  1. A.1, −1
  2. B.1, 2
  3. C.2, −2
  4. D.1, −2
Show the answer and explanation

Answer: D (1, −2)

Explanation

a*2 = a2, so a2 = 2 − a, i.e. a2 + a − 2 = 0. Factorising, (a − 1)(a + 2) = 0, so a = 1 or −2.