2026 GESS P2 Q2

2026 GESS P2 Q2

Secondary 4
7 marks

The term independent of \(x\) in the expansion of \(\left(x^2-\dfrac{k}{4x}\right)^9\), where \(k\) is a constant, is 5376.

  1. Find the value of \(k\).[4]
  2. Using your value of \(k\), find the coefficient of \(x^9\) in the expansion of \(\left(1-9x^9\right)\left(x^2-\dfrac{k}{4x}\right)^9\).[3]

Solution:

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Answer:(a) \(k=\pm8\). (b) \(-49056\) if \(k=8\); \(-47712\) if \(k=-8\).

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