OCR C2 2009 January — Question 7

Exam BoardOCR
ModuleC2 (Core Mathematics 2)
Year2009
SessionJanuary
TopicBinomial Theorem (positive integer n)
TypeTwo equations from coefficients

7 In the binomial expansion of \(( k + a x ) ^ { 4 }\) the coefficient of \(x ^ { 2 }\) is 24 .
  1. Given that \(a\) and \(k\) are both positive, show that \(a k = 2\).
  2. Given also that the coefficient of \(x\) in the expansion is 128 , find the values of \(a\) and \(k\).
  3. Hence find the coefficient of \(x ^ { 3 }\) in the expansion.