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WAEC Further Mathematics 2016 Question 3

Question 3

Binary Operations

An operation * is defined on the set, R, of real numbers by p * q = p + q + 2pq. If the identity element of the operation is zero, find the value of p for which the operation has no inverse.

  1. A.−½
  2. B.0
  3. C.⅔
  4. D.2
Show the answer and explanation

Answer: A (−½)

Explanation

The inverse q of p satisfies p + q + 2pq = 0, so q = −p/(1 + 2p). This fails only when 1 + 2p = 0, i.e. p = −½.