What is the value of q if the coefficients of x^{3} and x^{6} are equal?
Consider the following for the next three (03) items that follow : Consider the binomial expansion of (p+qx)^{9}:
- A. p ✓
- B. 9p
- C. \frac{1}{p}
- D. p^{2}
Correct Answer: A. p
Explanation
The coefficient of x^r in (p+qx)^9 is C(9,r) p^{9-r} q^r. Equating the coefficients for r=3 and r=6 gives C(9,3) p^6 q^3 = C(9,6) p^3 q^6. Since C(9,3) = C(9,6), this simplifies to p^3 = q^3, which implies q=p.
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