Given that the binomial expansion of $(1 + kx)^4$, |kx| < 1, is
1 - 6x + Ax^2 + .. - Edexcel - A-Level Maths Pure - Question 4 - 2014 - Paper 7
Question 4
Given that the binomial expansion of $(1 + kx)^4$, |kx| < 1, is
1 - 6x + Ax^2 + ...
(a) find the value of the constant k,
(b) find the value of the constant A, gi... show full transcript
Worked Solution & Example Answer:Given that the binomial expansion of $(1 + kx)^4$, |kx| < 1, is
1 - 6x + Ax^2 + .. - Edexcel - A-Level Maths Pure - Question 4 - 2014 - Paper 7
Step 1
find the value of the constant k
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Answer
To find the value of the constant k, we start with the binomial expansion of (1+kx)4:
(1+kx)4=1+4(kx)+6(kx)2+4(kx)3+(kx)4
From the given expansion, we know that the x coefficient is -6. Therefore, we need to equate this to the term 4(kx), which gives:
4k=−6
Solving for k:
k = rac{-6}{4} = - rac{3}{2}.
Step 2
find the value of the constant A, giving your answer in its simplest form
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Answer
Next, we will find the value of the constant A. From the binomial expansion, the coefficient for x2 is given by the term 6(kx)2:
