Find the value of *a* for which there is no term independent of *x* in the expansion of (1 + ax^2)(2/x - 3x)^6?

1 Answer
Apr 30, 2018

a = 2

Explanation:

(1 + ax^2)(2/x - 3x)
= (1 + ax^2)(729x^6 + 64/x^6 - 2916x^4 - 576/x^4 + 4860x^2 + 2160/x^2 -4320)

Upon expansion, the constant term must be eliminated to ensure complete dependence of the polynomial on x. Notice that the 2160/x^2 term becomes 2160a + 2160/x^2 upon expansion.
Setting a = 2 eliminates the constant as well as 2160a, which was independent of x. (4320 - 4320)

(Correct me if I'm wrong, please)