Question Detail
Question
In the expansion of (2x^2 + rx + 1)^6, the coefficients of x^2 and x^3 are 27 and -192 respectively. Find possible values of r.
Correct Answer
Option A is the correct answer.
Detailed Explanation
Use binomial formula: coefficient of x^2: C(6,2)(rx)^2(2x^2)^4, coefficient of x^3: C(6,3)(rx)^3(2x^2)^3 → solve system → r=-2 or 4.
Hint
Write general term T_k = C(6,k)*(2x^2)^(6-k)*(rx)^k.