Browse Questions

# If the coefficient of middle terms in $(1+\alpha x)^4$ and $(1-\alpha x)^6$ is same then $\alpha =?$

$\begin{array}{1 1} -\large\frac{5}{3} \\ -\large\frac{3}{10} \\ \large\frac{5}{3} \\ \large\frac{10}{3} \end{array}$

Toolbox:
• The midddle term in the expansion of $(1+x)^n$ is $(\large\frac{n}{2}+1)^{th}$ term
General term in the expansion of $(1+\alpha x)^4$ is $^4C_r\alpha^r x^r$
General term in the expansion of $(1-\alpha x)^6$ is $-^6C_r\alpha^r x^r$
The middle term in the expansion of $(1+\alpha x)^4$ is $3^{rd}$ term
The middle term in the expansion of $(1-\alpha x)^6$ is $4^{th}$ term
Given: $^4C_2\alpha^2$ = $-^6C_3\alpha^3$
$\Rightarrow\:\alpha=-\large\frac{^4C_2}{^6C_3}$ = $-\large\frac{6}{20}=-\large\frac{3}{10}$