Under what condition the coefficients of x^{2} and x^{4} are equal?
Consider the following for the next three (03) items that follow : Consider the binomial expansion of (p+qx)^{9}:
- A. p:q=7:2
- B. p^{2}:q^{2}=7:2 ✓
- C. p:q=2:7
- D. p^{2}:q^{2}=2:7
Correct Answer: B. p^{2}:q^{2}=7:2
Explanation
The coefficients of x^2 and x^4 are C(9,2) p^7 q^2 and C(9,4) p^5 q^4. Equating them gives 36 p^7 q^2 = 126 p^5 q^4. Dividing both sides by 18 p^5 q^2 yields 2p^2 = 7q^2, which gives p^2:q^2 = 7:2.
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