Edexcel P4 2022 June — Question 1

Exam BoardEdexcel
ModuleP4 (Pure Mathematics 4)
Year2022
SessionJune
TopicGeneralised Binomial Theorem
TypeTwo unknowns from two coefficient conditions

  1. The binomial expansion of
$$( 3 + k x ) ^ { - 2 } \quad | k x | < 3$$ where \(k\) is a non-zero constant, may be written in the form $$A + B x + C x ^ { 2 } + D x ^ { 3 } + \ldots$$ where \(A\), \(B\), \(C\) and \(D\) are constants.
  1. Find the value of \(A\) Given that \(C = 3 B\)
  2. show that $$k ^ { 2 } + 6 k = 0$$
  3. Hence (i) find the value of \(k\)
    (ii) find the value of \(D\)