SPS SPS SM Pure 2021 June — Question 6

Exam BoardSPS
ModuleSPS SM Pure (SPS SM Pure)
Year2021
SessionJune
TopicBinomial Theorem (positive integer n)
TypeRatio of coefficients condition

6. (a) Find the first 4 terms, in ascending powers of \(x\), in the binomial expansion of $$( 1 + k x ) ^ { 10 }$$ where \(k\) is a non-zero constant. Write each coefficient as simply as possible. Given that in the expansion of \(( 1 + k x ) ^ { 10 }\) the coefficient \(x ^ { 3 }\) is 3 times the coefficient of \(x\), (b) find the possible values of \(k\).